{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T15:54:58Z","timestamp":1772294098214,"version":"3.50.1"},"reference-count":92,"publisher":"Elsevier","isbn-type":[{"value":"9780444528490","type":"print"}],"license":[{"start":{"date-parts":[[2006,1,1]],"date-time":"2006-01-01T00:00:00Z","timestamp":1136073600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2006,1,1]],"date-time":"2006-01-01T00:00:00Z","timestamp":1136073600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2006]]},"DOI":"10.1016\/s1874-5725(06)80006-4","type":"book-chapter","created":{"date-parts":[[2007,9,7]],"date-time":"2007-09-07T22:50:27Z","timestamp":1189205427000},"page":"103-202","source":"Crossref","is-referenced-by-count":27,"title":["Chapter 2 Heteroclinic Orbits for Some Classes of Second and Fourth Order Differential Equations"],"prefix":"10.1016","member":"78","reference":[{"key":"10.1016\/S1874-5725(06)80006-4_bib1","series-title":"Pure and Applied Mathematics","article-title":"Sobolev Spaces","author":"Adams","year":"1975"},{"key":"10.1016\/S1874-5725(06)80006-4_bib2","doi-asserted-by":"crossref","first-page":"893","DOI":"10.1016\/0362-546X(91)90152-Q","article-title":"An elementary approach to traveling front solutions to a system ofN competition- diffusion equations","volume":"16","author":"Ahmad","year":"1991","journal-title":"Nonlinear Anal."},{"key":"10.1016\/S1874-5725(06)80006-4_bib3","doi-asserted-by":"crossref","first-page":"860","DOI":"10.1007\/s000330050184","article-title":"Multibump solutions to possibly degenerate equilibria for almost periodic Lagrangian systems","volume":"50","author":"Alessio","year":"1999","journal-title":"Z. Angew. Math. Phys."},{"key":"10.1016\/S1874-5725(06)80006-4_bib4","doi-asserted-by":"crossref","first-page":"569","DOI":"10.3934\/dcds.1999.5.569","article-title":"Heteroclinic motions joining almost periodic solutions for a class of Lagrangian systems","volume":"5","author":"Alessio","year":"1999","journal-title":"Discrete Contin. Dynam. Systems"},{"key":"10.1016\/S1874-5725(06)80006-4_bib5","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1007\/s005260000036","article-title":"Stationary layered solutions in R2 for a class of non au- tonomous Allen-Cahn equations","volume":"11","author":"Alessio","year":"2000","journal-title":"Calc. Var. Partial Differential Equations"},{"key":"10.1016\/S1874-5725(06)80006-4_bib6","doi-asserted-by":"crossref","first-page":"1537","DOI":"10.1081\/PDE-120005848","article-title":"Existence of infinitely many stationary layered solutions in R2 for a class of periodic Allen-Cahn equations","volume":"27","author":"Alessio","year":"2002","journal-title":"Comm. Partial Differential Equations"},{"key":"10.1016\/S1874-5725(06)80006-4_bib7","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1016\/s0294-1449(97)89300-6","article-title":"Homoclinics: Poincar\u00e9-Melnikov type results via a variational approach","volume":"15","author":"Ambrosetti","year":"1998","journal-title":"Ann. Inst. H. Poincar\u00e9 Anal. Non Lineaire"},{"key":"10.1016\/S1874-5725(06)80006-4_bib8","first-page":"1131","article-title":"Variational perturbative methods and bifurcation of bound states from the essential spectrum","volume":"A 128","author":"Ambrosetti","year":"1998"},{"key":"10.1016\/S1874-5725(06)80006-4_bib9","first-page":"601","article-title":"Multiplicit\u00e9 des orbites homoclines pour des syst\u00e8mes conservatifs","volume":"314","author":"Ambrosetti","year":"1992","journal-title":"C. R. Acad. Sci. Paris S\u00e9r. I Math."},{"key":"10.1016\/S1874-5725(06)80006-4_bib10","doi-asserted-by":"crossref","first-page":"319","DOI":"10.1007\/s00526-004-0264-y","article-title":"Fast and heteroclinic solutions for a second order ODE related to Fisher-Kolmogorov's equation","volume":"21","author":"Arias","year":"2004","journal-title":"Calc. Var. Partial Differential Equations"},{"key":"10.1016\/S1874-5725(06)80006-4_bib11","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1016\/0001-8708(78)90130-5","article-title":"Multidimensional nonlinear diffusion arising in population genetics","volume":"30","author":"Aronson","year":"1978","journal-title":"Adv. in Math."},{"key":"10.1016\/S1874-5725(06)80006-4_bib12","doi-asserted-by":"crossref","first-page":"1207","DOI":"10.1137\/0516088","article-title":"Traveling wave solutions to combustion models and their singular limits","volume":"16","author":"Berestycki","year":"1985","journal-title":"SIAM J. Math. Anal."},{"key":"10.1016\/S1874-5725(06)80006-4_bib13","first-page":"1169","article-title":"Multiplicity of homoclinic solutions for singular second-order conservative systems","volume":"A 126","author":"Bertotti","year":"1996"},{"key":"10.1016\/S1874-5725(06)80006-4_bib14","doi-asserted-by":"crossref","first-page":"453","DOI":"10.1006\/jdeq.1998.3415","article-title":"Connecting orbits for some classes of almost periodic Lagrangian sys- tems","volume":"145","author":"Bertotti","year":"1998","journal-title":"J. Differential Equations"},{"key":"10.1016\/S1874-5725(06)80006-4_bib15","first-page":"85","article-title":"Nouvelles recherches sur les systemes dynamiques","volume":"1","author":"Birkhoff","year":"1935","journal-title":"Mem. Pont. Acad. Sci. Novi Lycaei"},{"key":"10.1016\/S1874-5725(06)80006-4_bib16","first-page":"98","article-title":"Existence ofhomoclinic motions","author":"Bolotin","year":"1983","journal-title":"Vestnik Moskov. Univ. Ser. I Mat. Mekh."},{"key":"10.1016\/S1874-5725(06)80006-4_bib17","first-page":"230","article-title":"Variational methods for constructing chaotic motions in the dynamics of a rigid body","volume":"56","author":"Bolotin","year":"1992","journal-title":"Prikl. Mat. Mekh."},{"key":"10.1016\/S1874-5725(06)80006-4_bib18","doi-asserted-by":"crossref","first-page":"319","DOI":"10.1016\/j.anihpc.2003.03.001","article-title":"Multi-transition kinks and pulses for fourth order equations with a bistable nonlinearity","volume":"21","author":"Bonheure","year":"2004","journal-title":"Ann.Inst. H. Poincar\u00e9 Anal. Non Lin\u00e9aire"},{"key":"10.1016\/S1874-5725(06)80006-4_bib19","first-page":"213","article-title":"Minimizers for fourth order symmetric bistable equation","volume":"52","author":"Bonheure","year":"2004","journal-title":"Atti Sem. Mat. Fis. Univ. Modena e Reggio Emilia"},{"key":"10.1016\/S1874-5725(06)80006-4_bib20","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1007\/s00526-002-0172-y","article-title":"Heteroclinic connections between nonconsecutive equilibria of a fourth order differential equation","volume":"17","author":"Bonheure","year":"2003","journal-title":"Calc. Var. Partial Differential Equations"},{"key":"10.1016\/S1874-5725(06)80006-4_bib21","doi-asserted-by":"crossref","first-page":"673","DOI":"10.1016\/s0294-1449(00)00054-8","article-title":"A variational approach to chaotic dynamics in periodically forced nonlinear oscil- lators","volume":"17","author":"Bosetto","year":"2000","journal-title":"Ann. Inst. H. Poincar\u00e9 Anal. Non Lin\u00e9aire"},{"key":"10.1016\/S1874-5725(06)80006-4_bib22","series-title":"Collection math\u00e9matiques appliqu\u00e9es pour la ma\u00eetrise [Collection of Ap- plied Mathematics for the Master's Degree]","article-title":"Analyse fonctionnelle","author":"Brezis","year":"1983"},{"key":"10.1016\/S1874-5725(06)80006-4_bib23","doi-asserted-by":"crossref","first-page":"285","DOI":"10.1002\/(SICI)1097-0312(199603)49:3<285::AID-CPA3>3.0.CO;2-9","article-title":"A global condition for quasi-random behavior in a class of conservative systems","volume":"49","author":"Buffoni","year":"1996","journal-title":"Comm. Pure Appl. Math."},{"key":"10.1016\/S1874-5725(06)80006-4_bib24","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1007\/s005260050136","article-title":"Homoclinic solutions to periodic motions in a class of reversible equations","volume":"9","author":"Calanchi","year":"1999","journal-title":"Calc. Var. Partial Differential Equations"},{"key":"10.1016\/S1874-5725(06)80006-4_bib25","doi-asserted-by":"crossref","first-page":"76","DOI":"10.1006\/jdeq.1996.3230","article-title":"Homoclinics and heteroclinics for a class of conservative singular Hamiltonian systems","volume":"136","author":"Caldiroli","year":"1997","journal-title":"J. Differential Equations"},{"key":"10.1016\/S1874-5725(06)80006-4_bib26","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1006\/jdeq.1999.3633","article-title":"Existence and multiplicity results for heteroclinic orbits of second order Hamiltonian systems","volume":"158","author":"Chen","year":"1999","journal-title":"J. Differential Equations"},{"key":"10.1016\/S1874-5725(06)80006-4_bib27","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1007\/BF01444526","article-title":"A variational approach to homoclinic orbits in Hamiltonian systems","volume":"288","author":"Coti Zelati","year":"1990","journal-title":"Math. Ann."},{"key":"10.1016\/S1874-5725(06)80006-4_bib28","doi-asserted-by":"crossref","first-page":"693","DOI":"10.1090\/S0894-0347-1991-1119200-3","article-title":"Homoclinic orbits for second order Hamiltonian systems possessing superquadratic potentials","volume":"4","author":"Coti Zelati","year":"1991","journal-title":"J. Amer. Math. Soc."},{"key":"10.1016\/S1874-5725(06)80006-4_bib29","doi-asserted-by":"crossref","first-page":"1","DOI":"10.12775\/TMNA.2001.001","article-title":"Heteroclinic solutions between stationary points at different energy levels","volume":"17","author":"Coti Zelati","year":"2001","journal-title":"Topol. Methods Nonlinear Anal."},{"key":"10.1016\/S1874-5725(06)80006-4_bib30","doi-asserted-by":"crossref","first-page":"2641","DOI":"10.1103\/PhysRevLett.60.2641","article-title":"Bistable systems with propagating fronts leading to pattern formation","volume":"60","author":"Dee","year":"1988","journal-title":"Phys. Rev. Lett."},{"key":"10.1016\/S1874-5725(06)80006-4_bib31","doi-asserted-by":"crossref","first-page":"431","DOI":"10.1016\/0022-0396(76)90130-3","article-title":"Homoclinic orbits in Hamiltonian systems","volume":"21","author":"Devaney","year":"1976","journal-title":"J. Differential Equations"},{"key":"10.1016\/S1874-5725(06)80006-4_bib32","doi-asserted-by":"crossref","first-page":"503","DOI":"10.1016\/S1468-1218(02)00077-9","article-title":"Existence of travelling waves with their minimal speed for a diffusing Lotka-Volterra system","volume":"4","author":"Fei","year":"2003","journal-title":"Nonlinear Anal. Real World Appl."},{"key":"10.1016\/S1874-5725(06)80006-4_bib33","doi-asserted-by":"crossref","first-page":"335","DOI":"10.1007\/BF00250432","article-title":"The approach of solutions of nonlinear diffusion equations to travelling front solutions","volume":"65","author":"Fife","year":"1977","journal-title":"Arch. Ration. Mech. Anal."},{"key":"10.1016\/S1874-5725(06)80006-4_bib34","doi-asserted-by":"crossref","first-page":"355","DOI":"10.1111\/j.1469-1809.1937.tb02153.x","article-title":"The wave of advance of advantageous genes","volume":"7","author":"Fisher","year":"1937","journal-title":"Ann. Eugenics"},{"key":"10.1016\/S1874-5725(06)80006-4_bib35","series-title":"Progress in Nonlinear Differential Equations and their Applications","article-title":"Travelling Waves in Nonlinear Diffusion-Convection Reaction","author":"Gilding","year":"2004"},{"key":"10.1016\/S1874-5725(06)80006-4_bib36","series-title":"Phase Transitions and Critical Phenomena","first-page":"1","article-title":"Self-assembling amphiphilic systems","author":"Gompper","year":"1994"},{"key":"10.1016\/S1874-5725(06)80006-4_bib37","series-title":"Proceedings of Equadiff 10","first-page":"203","article-title":"Heteroclinics for a class of fourth order conservative differential equations","author":"Habets","year":"2001"},{"key":"10.1016\/S1874-5725(06)80006-4_bib38","series-title":"Texts in Applied Mathematics","article-title":"Dynamics and Bifurcations","author":"Hale","year":"1991"},{"key":"10.1016\/S1874-5725(06)80006-4_bib39","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1007\/PL00004238","article-title":"Travelling fronts and entire solutions of the Fisher-KPP equation in RN","volume":"157","author":"Hamel","year":"2001","journal-title":"Arch. Ration. Mech. Anal."},{"key":"10.1016\/S1874-5725(06)80006-4_bib40","series-title":"Cambridge Mathematical Library","article-title":"Inequalities","author":"Hardy","year":"1988"},{"key":"10.1016\/S1874-5725(06)80006-4_bib41","series-title":"Ordinary Differential Equations","author":"Hartman","year":"1964"},{"key":"10.1016\/S1874-5725(06)80006-4_bib42","doi-asserted-by":"crossref","first-page":"337","DOI":"10.1007\/s002200050332","article-title":"Homotopy classes for stable connections between Hamiltonian saddle-focus equilibria","volume":"193","author":"Kalies","year":"1998","journal-title":"Comm. Math. Phys."},{"key":"10.1016\/S1874-5725(06)80006-4_bib43","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1006\/jdeq.1996.0161","article-title":"Multi-transition homoclinic and heteroclinic solutions of the extended Fisher-Kolmogorov equation","volume":"131","author":"Kalies","year":"1996","journal-title":"J. Differential Equations"},{"key":"10.1016\/S1874-5725(06)80006-4_bib44","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1080\/00036819408840304","article-title":"Analytic approximations of travelling wave solutions","volume":"55","author":"Kelley","year":"1994","journal-title":"Appl. Anal."},{"key":"10.1016\/S1874-5725(06)80006-4_bib45","first-page":"1","article-title":"Etude de l'\u00e9quation de la diffusion avec croissance de la quantit\u00e9 de mati\u00e8re et son application \u00e0 un probl\u00e8me biologique","volume":"1","author":"Kolmogorov","year":"1937","journal-title":"Bull. Univ. Moskou Ser. Internat. Sec. A"},{"key":"10.1016\/S1874-5725(06)80006-4_bib46","doi-asserted-by":"crossref","first-page":"357","DOI":"10.57262\/die\/1367526342","article-title":"On homoclinic and heteroclinic orbits for Hamiltonian systems","volume":"10","author":"Korman","year":"1997","journal-title":"Differential Integral Equations"},{"key":"10.1016\/S1874-5725(06)80006-4_bib47","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1006\/jdeq.1999.3750","article-title":"Uniqueness of the stationary wave for the extended Fisher-Kolmogorov equation","volume":"165","author":"Kwapisz","year":"2000","journal-title":"J. Differential Equations"},{"key":"10.1016\/S1874-5725(06)80006-4_bib48","doi-asserted-by":"crossref","first-page":"575","DOI":"10.3934\/dcds.2000.6.575","article-title":"Existence of bounded trajectories via upper and lower solutions","volume":"6","author":"Malaguti","year":"2000","journal-title":"Discrete Contin. Dynam. Systems"},{"key":"10.1016\/S1874-5725(06)80006-4_bib49","doi-asserted-by":"crossref","first-page":"148","DOI":"10.1002\/1522-2616(200207)242:1<148::AID-MANA148>3.0.CO;2-J","article-title":"Travelling wavefronts in reaction-diffusion equations with convection effects and non-regular terms","volume":"242","author":"Malaguti","year":"2002","journal-title":"Math. Nachr."},{"key":"10.1016\/S1874-5725(06)80006-4_bib50","article-title":"Existence and multiplicity of heteroclinic solutions for a non-autonomous boundary eigenvalue problem","author":"Malaguti","year":"2003","journal-title":"Electron. J. Differential Equations"},{"key":"10.1016\/S1874-5725(06)80006-4_bib51","doi-asserted-by":"crossref","first-page":"471","DOI":"10.1016\/j.jde.2003.06.005","article-title":"Sharp profiles in degenerate and doubly degenerate Fisher-KPP equations","volume":"195","author":"Malaguti","year":"2003","journal-title":"J. Differential Equations"},{"key":"10.1016\/S1874-5725(06)80006-4_bib52","series-title":"Dynamical systems","first-page":"231","article-title":"Travelling waves in spatially discrete dynamicalsystem of difusive type","author":"Mallet-Paret","year":"2003"},{"key":"10.1016\/S1874-5725(06)80006-4_bib53","doi-asserted-by":"crossref","first-page":"871","DOI":"10.1016\/0362-546X(95)00193-Y","article-title":"Heteroclinic chains for a reversible Hamiltonian system","volume":"28","author":"Maxwell","year":"1997","journal-title":"Nonlinear Anal."},{"key":"10.1016\/S1874-5725(06)80006-4_bib54","first-page":"3","article-title":"On the stability of a center for time-periodic perturbations","volume":"12","author":"Mel'nikov","year":"1963","journal-title":"Trudy Moskov. Mat. Ob<s<c."},{"key":"10.1016\/S1874-5725(06)80006-4_bib55","doi-asserted-by":"crossref","first-page":"343","DOI":"10.1007\/s002050050133","article-title":"Periodic phases in second-order materials","volume":"145","author":"Mizel","year":"1998","journal-title":"Arch. Ration. Mech.Anal."},{"key":"10.1016\/S1874-5725(06)80006-4_bib56","doi-asserted-by":"crossref","first-page":"3713","DOI":"10.1090\/S0002-9947-99-02249-7","article-title":"A global condition for periodic Duffing-like equations","volume":"351","author":"Montecchiari","year":"1999","journal-title":"Trans. Amer. Math. Soc."},{"key":"10.1016\/S1874-5725(06)80006-4_bib57","series-title":"Ann. Math. Studies","article-title":"Stable and Random Motions in Dynamical Systems: With Special Emphasis on Celestial Mechanics","author":"Moser","year":"1973"},{"key":"10.1016\/S1874-5725(06)80006-4_bib58","first-page":"327","article-title":"Stationary solutions of a fourth-order nonlinear diffusion equation","volume":"31","author":"Peletier","year":"1995","journal-title":"Differentsial'nye Uravneniya"},{"key":"10.1016\/S1874-5725(06)80006-4_bib59","doi-asserted-by":"crossref","first-page":"1279","DOI":"10.57262\/die\/1368638166","article-title":"Spatial patterns described by the extended Fisher-Kolmogorov (EFK) equation: kinks","volume":"8","author":"Peletier","year":"1995","journal-title":"Differential Integral Equations"},{"key":"10.1016\/S1874-5725(06)80006-4_bib60","doi-asserted-by":"crossref","first-page":"331","DOI":"10.12775\/TMNA.1995.049","article-title":"A topological shooting method and the existence of kinks of the extended Fisher-Kolmogorov equation","volume":"6","author":"Peletier","year":"1995","journal-title":"Topol. Methods Nonlinear Anal."},{"key":"10.1016\/S1874-5725(06)80006-4_bib61","doi-asserted-by":"crossref","first-page":"458","DOI":"10.1006\/jdeq.1996.0124","article-title":"Chaotic spatial patterns described by the extended Fisher-Kolmogorov equation","volume":"129","author":"Peletier","year":"1996","journal-title":"J. Differential Equations"},{"key":"10.1016\/S1874-5725(06)80006-4_bib62","doi-asserted-by":"crossref","first-page":"1317","DOI":"10.1137\/S0036141095280955","article-title":"Spatial patterns described by the extended Fisher-Kolmogorov equation: periodic solutions","volume":"28","author":"Peletier","year":"1997","journal-title":"SIAM J. Math. Anal."},{"key":"10.1016\/S1874-5725(06)80006-4_bib63","series-title":"Progress in Nonlinear Differential Equations and their Applications","article-title":"Spatial Patterns","author":"Peletier","year":"2001"},{"key":"10.1016\/S1874-5725(06)80006-4_bib64","series-title":"Les m\u00e9thodes nouvelles de la m\u00e9canique c\u00e9leste","author":"Poincar\u00e9","year":"1957"},{"key":"10.1016\/S1874-5725(06)80006-4_bib65","series-title":"Maximum Principles in Differential Equations","author":"Protter","year":"1967"},{"key":"10.1016\/S1874-5725(06)80006-4_bib66","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1016\/s0294-1449(16)30314-6","article-title":"Periodic and heteroclinic orbits for a periodic Hamiltonian system","volume":"6","author":"Rabinowitz","year":"1989","journal-title":"Ann. Inst. H. Poincar\u00e9 Anal. Non Lineaire"},{"key":"10.1016\/S1874-5725(06)80006-4_bib67","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BF02163262","article-title":"Homoclinic and heteroclinic orbits for a class of Hamiltonian systems","volume":"1","author":"Rabinowitz","year":"1993","journal-title":"Calc. Var. Partial Differential Equations"},{"key":"10.1016\/S1874-5725(06)80006-4_bib68","doi-asserted-by":"crossref","first-page":"1557","DOI":"10.57262\/die\/1369329531","article-title":"Heteroclinics for a reversible Hamiltonian system. II","volume":"7","author":"Rabinowitz","year":"1994","journal-title":"Differential Integral Equations"},{"key":"10.1016\/S1874-5725(06)80006-4_bib69","doi-asserted-by":"crossref","first-page":"49","DOI":"10.12775\/TMNA.1995.031","article-title":"Homoclinic s for an almost periodically forced singular Hamiltonian system","volume":"6","author":"Rabinowitz","year":"1995","journal-title":"Topol. Methods Nonlinear Anal."},{"key":"10.1016\/S1874-5725(06)80006-4_bib70","doi-asserted-by":"crossref","first-page":"399","DOI":"10.1007\/PL00009919","article-title":"On a theorem of Strobel","volume":"12","author":"Rabinowitz","year":"2001","journal-title":"Calc. Var. Partial Differential Equations"},{"key":"10.1016\/S1874-5725(06)80006-4_bib71","doi-asserted-by":"crossref","first-page":"507","DOI":"10.3934\/dcds.2004.10.507","article-title":"A new variational characterization of spatially heteroclinic solutions of a semilinear elliptic PDE","volume":"10","author":"Rabinowitz","year":"2004","journal-title":"Discrete Contin. Dyn. Syst."},{"key":"10.1016\/S1874-5725(06)80006-4_bib72","series-title":"Proceedings of the Conference on Nonlinear Differential Equations","first-page":"223","article-title":"Multichain-type solutions for Hamiltonian systems","author":"Rabinowitz","year":"2000"},{"key":"10.1016\/S1874-5725(06)80006-4_bib73","doi-asserted-by":"crossref","first-page":"1078","DOI":"10.1002\/cpa.10087","article-title":"Mixed states for an Allen-Cahn type equation","volume":"56","author":"Rabinowitz","year":"2003","journal-title":"Comm. Pure Appl.Math."},{"key":"10.1016\/S1874-5725(06)80006-4_bib74","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1007\/s00526-003-0251-8","article-title":"Mixed states for an Allen-Cahn type equation. II","volume":"21","author":"Rabinowitz","year":"2004","journal-title":"Calc. Var. Partial Differential Equations"},{"key":"10.1016\/S1874-5725(06)80006-4_bib75","doi-asserted-by":"crossref","first-page":"532","DOI":"10.1006\/jdeq.2000.3984","article-title":"Existence and stability of traveling fronts in the extended FisherKolmogorov equation","volume":"176","author":"Rottsch\u00e4fer","year":"2001","journal-title":"J. Differential Equations"},{"key":"10.1016\/S1874-5725(06)80006-4_bib76","series-title":"Monographs and Textbooks in Pure and Applied Mathematics","article-title":"Nonlinear Ordinary Differential Equations and their Applications","author":"Sachdev","year":"1991"},{"key":"10.1016\/S1874-5725(06)80006-4_bib77","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1016\/S0377-0427(99)00254-X","article-title":"A note on a nonautonomous O.D.E. related to the Fisher equation","author":"Sanchez","year":"2000","journal-title":"J. Comput. Appl. Math. 113"},{"key":"10.1016\/S1874-5725(06)80006-4_bib78","series-title":"Proceedings of the USA- Chile Workshop on Nonlinear Analysis","first-page":"257","article-title":"Heteroclinic connections for a class of non-autonomous systems","author":"Sanchez","year":"2001"},{"key":"10.1016\/S1874-5725(06)80006-4_bib79","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1007\/BF02570817","article-title":"Existence of infinitely many homoclinic orbits in Hamiltonian systems","volume":"209","author":"S\u00e9r\u00e9","year":"1992","journal-title":"Math. Z."},{"key":"10.1016\/S1874-5725(06)80006-4_bib80","first-page":"615","article-title":"Heteroclinic orbits at infinity for two classes of Hamiltonian systems","volume":"8","author":"Serra","year":"1994","journal-title":"Boll. Un. Mat. Ital. B (7)"},{"key":"10.1016\/S1874-5725(06)80006-4_bib81","series-title":"Differential and Combinatorial Topology","first-page":"63","article-title":"Diffeomorphisms with many periodic points","author":"Smale","year":"1965"},{"key":"10.1016\/S1874-5725(06)80006-4_bib82","doi-asserted-by":"crossref","first-page":"747","DOI":"10.1090\/S0002-9904-1967-11798-1","article-title":"Differentiate dynamical systems","volume":"73","author":"Smale","year":"1967","journal-title":"Bull. Amer. Math. Soc."},{"key":"10.1016\/S1874-5725(06)80006-4_bib83","doi-asserted-by":"crossref","first-page":"78","DOI":"10.1006\/jdeq.2001.4135","article-title":"Homoclinic solutions for Swift-Hohenberg and suspension bridge type equations","volume":"184","author":"Smets","year":"2002","journal-title":"J. Differential Equations"},{"key":"10.1016\/S1874-5725(06)80006-4_bib84","doi-asserted-by":"crossref","first-page":"319","DOI":"10.1103\/PhysRevA.15.319","article-title":"Hydrodynamic fluctuations at the convective instability","volume":"A 15","author":"Swift","year":"1977","journal-title":"Phys. Rev."},{"key":"10.1016\/S1874-5725(06)80006-4_bib85","doi-asserted-by":"crossref","first-page":"427","DOI":"10.1016\/s0294-1449(16)30285-2","article-title":"Homoclinic orbits for a singular second order Hamiltonian system","volume":"7","author":"Tanaka","year":"1990","journal-title":"Ann. Inst. H. Poincar\u00e9 Anal. Non Lin\u00e9aire"},{"key":"10.1016\/S1874-5725(06)80006-4_bib86","doi-asserted-by":"crossref","first-page":"337","DOI":"10.1016\/S0362-546X(98)00051-0","article-title":"Non-degeneracy and chaotic motions for a class of almost-periodic Lagrangean systems","volume":"37","author":"Terracim","year":"1999","journal-title":"Non- linear Anal."},{"key":"10.1016\/S1874-5725(06)80006-4_bib87","article-title":"Branches of heteroclinic homoclinic and periodic solutions in a fourth-order bistable system, a numerical study","author":"van den Berg","year":"1996"},{"key":"10.1016\/S1874-5725(06)80006-4_bib88","article-title":"Dynamics and equilibria of fourth order differential equations","author":"van den Berg","year":"2000"},{"key":"10.1016\/S1874-5725(06)80006-4_bib89","doi-asserted-by":"crossref","first-page":"110","DOI":"10.1006\/jdeq.1999.3698","article-title":"The phase-plane picture for a class of fourth-order conservative differential equations","volume":"161","author":"van den Berg","year":"2000","journal-title":"J. Differential Equations"},{"key":"10.1016\/S1874-5725(06)80006-4_bib90","doi-asserted-by":"crossref","first-page":"1342","DOI":"10.1137\/S0036141099358300","article-title":"Traveling waves for fourth order parabolic equations","volume":"32","author":"van den Berg","year":"2001","journal-title":"SIAM J. Math. Anal."},{"key":"10.1016\/S1874-5725(06)80006-4_bib91","series-title":"Graduate Texts in Mathematics","article-title":"Ordinary Differential Equations","author":"Walter","year":"1998"},{"key":"10.1016\/S1874-5725(06)80006-4_bib92","series-title":"Applied Mathematical Sciences","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-1042-9","article-title":"Global bifurcations and chaos","author":"Wiggins","year":"1988"}],"container-title":["Handbook of Differential Equations: Ordinary Differential Equations"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S1874572506800064?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S1874572506800064?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2025,10,29]],"date-time":"2025-10-29T12:47:40Z","timestamp":1761742060000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S1874572506800064"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006]]},"ISBN":["9780444528490"],"references-count":92,"URL":"https:\/\/doi.org\/10.1016\/s1874-5725(06)80006-4","relation":{},"ISSN":["1874-5725"],"issn-type":[{"value":"1874-5725","type":"print"}],"subject":[],"published":{"date-parts":[[2006]]}}}