{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,29]],"date-time":"2022-03-29T00:52:07Z","timestamp":1648515127375},"reference-count":28,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2014,10,9]],"date-time":"2014-10-09T00:00:00Z","timestamp":1412812800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Sci Comput"],"published-print":{"date-parts":[[2015,7]]},"DOI":"10.1007\/s10915-014-9925-y","type":"journal-article","created":{"date-parts":[[2014,10,8]],"date-time":"2014-10-08T08:19:28Z","timestamp":1412756368000},"page":"109-129","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A New Approach for Numerically Solving Nonlinear Eigensolution Problems"],"prefix":"10.1007","volume":"64","author":[{"given":"Changchun","family":"Wang","sequence":"first","affiliation":[]},{"given":"Jianxin","family":"Zhou","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2014,10,9]]},"reference":[{"key":"9925_CR1","volume-title":"Nonlinear Fiber Optics","author":"GP Agrawal","year":"2013","unstructured":"Agrawal, G.P.: Nonlinear Fiber Optics, 5th edn. Academic Press, Oxford (2013)","edition":"5"},{"key":"9925_CR2","doi-asserted-by":"crossref","first-page":"7874","DOI":"10.1016\/j.jcp.2010.07.001","volume":"229","author":"W Bao","year":"2010","unstructured":"Bao, W., Cai, Y., Wang, H.: Efficient numerical methods for computing ground states and dynamics of dipolar Bose\u2013Einstein condensates. J. Comput. Phys. 229, 7874\u20137892 (2010)","journal-title":"J. Comput. Phys."},{"key":"9925_CR3","doi-asserted-by":"crossref","first-page":"1674","DOI":"10.1137\/S1064827503422956","volume":"25","author":"W Bao","year":"2004","unstructured":"Bao, W., Du, Q.: Computing the ground state solution of Bose\u2013Einstein condensates by a normalized gradient flow. SIAM J. Sci. Comput. 25, 1674\u20131697 (2004)","journal-title":"SIAM J. Sci. Comput."},{"key":"9925_CR4","first-page":"1","volume":"30","author":"T Bodurov","year":"2005","unstructured":"Bodurov, T.: Derivation of the nonlinear Schrodinger equation from first principle. Annales de la Fondation Louis de Broglie 30, 1\u201310 (2005)","journal-title":"Annales de la Fondation Louis de Broglie"},{"key":"9925_CR5","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1137\/0903012","volume":"3","author":"TFC Chan","year":"1982","unstructured":"Chan, T.F.C., Keller, H.B.: Arc-length continuation and multi-grid techniques for nonlinear elliptic eigenvalue problems. SIAM J. Sci. Stat. Comput. 3, 173\u2013194 (1982)","journal-title":"SIAM J. Sci. Stat. Comput."},{"key":"9925_CR6","volume-title":"Handbook of Differential Equations: Stationary Partial Differential Equations","year":"2008","unstructured":"Chipot, M. (ed.): Handbook of Differential Equations: Stationary Partial Differential Equations, vol. 5. Elsevier, Oxford (2008)"},{"key":"9925_CR7","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1016\/0362-546X(88)90012-0","volume":"12","author":"SN Chow","year":"1988","unstructured":"Chow, S.N., Lauterbach, R.: A bifurcation theorem for critical points of variational problems. Nonlinear Anal. 12, 51\u201361 (1988)","journal-title":"Nonlinear Anal."},{"key":"9925_CR8","doi-asserted-by":"crossref","first-page":"475","DOI":"10.1051\/m2an\/2013116","volume":"48","author":"Y Efendiev","year":"2014","unstructured":"Efendiev, Y., Galvis, J., Presho, M., Zhou, J.: A multiscale enrichment procedure for nonlinear monotone operators. M2AN 48, 475\u2013491 (2014)","journal-title":"M2AN"},{"key":"9925_CR9","doi-asserted-by":"crossref","unstructured":"Glowinski, R., Tallec, P.L.: Augmented Lagrangian and Operator-Splitting Methods in Nonlinear Mechanics. SIAM Studies in Applied Mathematics, vol. 9. SIAM, Philadelphia (1989)","DOI":"10.1137\/1.9781611970838"},{"key":"9925_CR10","doi-asserted-by":"crossref","first-page":"739","DOI":"10.1215\/S0012-7094-96-08423-9","volume":"84","author":"C Gui","year":"1996","unstructured":"Gui, C.: Multipeak solutions for a semilinear Neumann problem. Duke Math. J. 84, 739\u2013769 (1996)","journal-title":"Duke Math. J."},{"key":"9925_CR11","first-page":"359","volume-title":"Applications of Bifurcation Theory","author":"HB Keller","year":"1977","unstructured":"Keller, H.B.: Numerical solution of bifurcation and nonlinear eigenvalue problems. In: Rabinowitz, P. (ed.) Applications of Bifurcation Theory, pp. 359\u2013384. Academic Press, New York (1977)"},{"key":"9925_CR12","doi-asserted-by":"crossref","first-page":"840","DOI":"10.1137\/S1064827599365641","volume":"23","author":"Y Li","year":"2001","unstructured":"Li, Y., Zhou, J.: A minimax method for finding multiple critical points and its applications to semilinear elliptic PDEs. SIAM Sci. Comput. 23, 840\u2013865 (2001)","journal-title":"SIAM Sci. Comput."},{"key":"9925_CR13","doi-asserted-by":"crossref","unstructured":"Lin, C. S., Ni, W. M., Takagi, I.: Large amplitude stationary solutions to a chemotaxis system. J. Differ. Equ. 72, 1\u201327 (1988)","DOI":"10.1016\/0022-0396(88)90147-7"},{"key":"9925_CR14","doi-asserted-by":"crossref","first-page":"351","DOI":"10.1090\/S0002-9947-1986-0849484-2","volume":"297","author":"WM Ni","year":"1986","unstructured":"Ni, W.M., Takagi, I.: On the Neumann probem for some semilinear elliptic equations and systems of activator\u2013inhibitor type. Trans. Am. Math. Soc. 297, 351\u2013368 (1986)","journal-title":"Trans. Am. Math. Soc."},{"key":"9925_CR15","doi-asserted-by":"crossref","unstructured":"Rabinowitz, P.: Minimax method in critical point theory with applications to differential equations. In: CBMS Regional Conference Series in Mathematics, No. 65. AMS, Providence (1986)","DOI":"10.1090\/cbms\/065"},{"key":"9925_CR16","doi-asserted-by":"crossref","first-page":"255","DOI":"10.1016\/0270-0255(80)90061-5","volume":"1","author":"EWC Groesen Van","year":"1980","unstructured":"Van Groesen, E.W.C., Nijmegen, T.: Continuation of solutions of constrained extremum problems and nonlinear eigenvalue problems. Math. Model. 1, 255\u2013270 (1980)","journal-title":"Math. Model."},{"key":"9925_CR17","doi-asserted-by":"crossref","first-page":"891","DOI":"10.1137\/S0036142903416626","volume":"43","author":"ZQ Wang","year":"2005","unstructured":"Wang, Z.Q., Zhou, J.: An efficient and stable method for computing multiple saddle points with symmetries. SIAM J. Numer. Anal. 43, 891\u2013907 (2005)","journal-title":"SIAM J. Numer. Anal."},{"key":"9925_CR18","doi-asserted-by":"crossref","first-page":"1745","DOI":"10.1137\/S0036142903431675","volume":"42","author":"ZQ Wang","year":"2004","unstructured":"Wang, Z.Q., Zhou, J.: A local Minimax\u2013Newton method for finding critical points with symmetries. SIAM J. Numer. Anal. 42, 1745\u20131759 (2004)","journal-title":"SIAM J. Numer. Anal."},{"issue":"1","key":"9925_CR19","doi-asserted-by":"crossref","first-page":"142","DOI":"10.1088\/0031-8949\/1982\/T2A\/017","volume":"T2","author":"T Watanabe","year":"1982","unstructured":"Watanabe, T., Nishikawa, K., Kishimoto, Y., Hojo, H.: Numerical method for nonlinear eigenvalue problems. Phys. Scripta. T2(1), 142\u2013146 (1982)","journal-title":"Phys. Scripta."},{"key":"9925_CR20","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-4146-1","volume-title":"Minimax Theorems","author":"M Willem","year":"1996","unstructured":"Willem, M.: Minimax Theorems. Birkhauser, Boston (1996)"},{"key":"9925_CR21","doi-asserted-by":"crossref","first-page":"395","DOI":"10.1137\/100810411","volume":"34","author":"Z Xie","year":"2012","unstructured":"Xie, Z., Yuan, Y., Zhou, J.: On finding multiple solutions to a singularly perturbed neumann problem. SIAM J. Sci. Comput. 34, 395\u2013420 (2012)","journal-title":"SIAM J. Sci. Comput."},{"key":"9925_CR22","doi-asserted-by":"crossref","first-page":"1796","DOI":"10.1137\/S1064827503430503","volume":"26","author":"X Yao","year":"2005","unstructured":"Yao, X., Zhou, J.: A minimax method for finding multiple critical points in Banach spaces and its application to quasilinear elliptic PDE. SIAM J. Sci. Comput. 26, 1796\u20131809 (2005)","journal-title":"SIAM J. Sci. Comput."},{"key":"9925_CR23","doi-asserted-by":"crossref","first-page":"1355","DOI":"10.1137\/060651859","volume":"29","author":"X Yao","year":"2007","unstructured":"Yao, X., Zhou, J.: Numerical methods for computing nonlinear eigenpairs. Part I. Iso-homogenous cases. SIAM J. Sci. Comput. 29, 1355\u20131374 (2007)","journal-title":"SIAM J. Sci. Comput."},{"key":"9925_CR24","doi-asserted-by":"crossref","first-page":"937","DOI":"10.1137\/060656425","volume":"30","author":"X Yao","year":"2008","unstructured":"Yao, X., Zhou, J.: Numerical methods for computing nonlinear eigenpairs. Part II. Non iso-homogenous cases. SIAM J. Sci. Comput. 30, 937\u2013956 (2008)","journal-title":"SIAM J. Sci. Comput."},{"key":"9925_CR25","doi-asserted-by":"crossref","first-page":"238","DOI":"10.1002\/mana.19861290121","volume":"129","author":"E Zeidler","year":"1986","unstructured":"Zeidler, E.: Ljusternik\u2013Schnirelman theory on general level sets. Math. Nachr. 129, 238\u2013259 (1986)","journal-title":"Math. Nachr."},{"key":"9925_CR26","doi-asserted-by":"crossref","first-page":"66","DOI":"10.1016\/j.jmaa.2003.10.043","volume":"291","author":"J Zhou","year":"2004","unstructured":"Zhou, J.: A local min-orthogonal method for finding multiple saddle points. J. Math. Anal. Appl. 291, 66\u201381 (2004)","journal-title":"J. Math. Anal. Appl."},{"key":"9925_CR27","doi-asserted-by":"crossref","first-page":"1391","DOI":"10.1090\/S0025-5718-04-01694-1","volume":"74","author":"J Zhou","year":"2005","unstructured":"Zhou, J.: Instability analysis of saddle points by a local minimax method. Math. Comput. 74, 1391\u20131411 (2005)","journal-title":"Math. Comput."},{"key":"9925_CR28","doi-asserted-by":"crossref","first-page":"1365","DOI":"10.1080\/01630563.2011.597630","volume":"32","author":"J Zhou","year":"2011","unstructured":"Zhou, J.: Global sequence convergence of a local minimax method for finding multiple solutions in Banach spaces. Num. Func. Anal. Optim. 32, 1365\u20131380 (2011)","journal-title":"Num. Func. Anal. Optim."}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-014-9925-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10915-014-9925-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-014-9925-y","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,2]],"date-time":"2019-06-02T04:45:49Z","timestamp":1559450749000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10915-014-9925-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,10,9]]},"references-count":28,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2015,7]]}},"alternative-id":["9925"],"URL":"https:\/\/doi.org\/10.1007\/s10915-014-9925-y","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"value":"0885-7474","type":"print"},{"value":"1573-7691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,10,9]]}}}