{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T03:21:15Z","timestamp":1740108075212,"version":"3.37.3"},"reference-count":34,"publisher":"Springer Science and Business Media LLC","issue":"16","license":[{"start":{"date-parts":[[2020,1,24]],"date-time":"2020-01-24T00:00:00Z","timestamp":1579824000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,1,24]],"date-time":"2020-01-24T00:00:00Z","timestamp":1579824000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Neural Comput &amp; Applic"],"published-print":{"date-parts":[[2020,8]]},"DOI":"10.1007\/s00521-020-04732-x","type":"journal-article","created":{"date-parts":[[2020,1,24]],"date-time":"2020-01-24T12:02:36Z","timestamp":1579867356000},"page":"12873-12879","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Lidstone-type problems on the whole real line and homoclinic solutions applied to infinite beams"],"prefix":"10.1007","volume":"32","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7485-2500","authenticated-orcid":false,"given":"Feliz","family":"Minh\u00f3s","sequence":"first","affiliation":[]},{"given":"Hugo","family":"Carrasco","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,1,24]]},"reference":[{"key":"4732_CR1","first-page":"542","volume":"113","author":"G Adams","year":"1986","unstructured":"Adams G, Lin L (1986) Beam on a tensionless elastic foundation. J Eng Mech 113:542\u2013553","journal-title":"J Eng Mech"},{"key":"4732_CR2","doi-asserted-by":"publisher","first-page":"49","DOI":"10.1186\/1687-2770-2012-49","volume":"2012","author":"RP Agarwal","year":"2012","unstructured":"Agarwal RP, Wong PJ (2012) Eigenvalues of complementary Lidstone boundary value problems. Bound Value Probl 2012:49","journal-title":"Bound Value Probl"},{"key":"4732_CR3","doi-asserted-by":"publisher","first-page":"60","DOI":"10.1186\/1687-1847-2012-60","volume":"2012","author":"RP Agarwal","year":"2012","unstructured":"Agarwal RP, Wong PJ (2012) Positive solutions of complementary Lidstone boundary value problems. Electron J Qual Theory Differ Equ 2012:60","journal-title":"Electron J Qual Theory Differ Equ"},{"key":"4732_CR4","doi-asserted-by":"publisher","first-page":"442","DOI":"10.1016\/S0022-247X(03)00011-8","volume":"279","author":"Z Bai","year":"2003","unstructured":"Bai Z, Ge W (2003) Solutions of 2nth Lidstone boundary value problems and dependence on higher order derivatives. J Math Anal Appl 279:442\u2013450","journal-title":"J Math Anal Appl"},{"key":"4732_CR5","doi-asserted-by":"publisher","first-page":"123","DOI":"10.1016\/j.cnsns.2016.12.010","volume":"48","author":"YY Chen","year":"2017","unstructured":"Chen YY, Chen SH, Zhao W (2017) Constructing explicit homoclinic solution of oscillators: an improvement for perturbation procedure based on nonlinear time transformation. Commun Nonlinear Sci Numer Simul 48:123\u2013139","journal-title":"Commun Nonlinear Sci Numer Simul"},{"issue":"19","key":"4732_CR6","doi-asserted-by":"publisher","first-page":"3071","DOI":"10.1177\/1077546315573915","volume":"23","author":"YY Chen","year":"2017","unstructured":"Chen YY, Yan LW, Su RKL, Liu B (2017) Generalization of hyperbolic perturbation solution for heteroclinic orbits of strongly nonlinear self-excited oscillator. J Vib Control 23(19):3071\u20133091","journal-title":"J Vib Control"},{"key":"4732_CR7","doi-asserted-by":"publisher","first-page":"527","DOI":"10.1006\/jmaa.2000.7028","volume":"251","author":"JM Davis","year":"2000","unstructured":"Davis JM, Henderson J, Wong P (2000) General Lidstone problems: multiplicity and symmetry of solutions. J Math Anal Appl 251:527\u2013548","journal-title":"J Math Anal Appl"},{"issue":"2","key":"4732_CR8","doi-asserted-by":"publisher","first-page":"48","DOI":"10.12816\/0006104","volume":"5","author":"Y Ding","year":"2012","unstructured":"Ding Y, Wei Z, Xu J (2012) Positive solutions for a higher order p-Laplacian boundary value problem with even derivatives. Int J Open Probl Comput Math 5(2):48\u201361","journal-title":"Int J Open Probl Comput Math"},{"key":"4732_CR9","unstructured":"Ehme J, Henderson J (2000) Existence and local uniqueness for nonlinear Lidstone boundary value problems. J Inequal Pure Appl Math 1(1), Article 8, 1\u20139"},{"issue":"2000","key":"4732_CR10","first-page":"1","volume":"2","author":"P Eloe","year":"2000","unstructured":"Eloe P (2000) Nonlinear eigenvalue problems for higher order Lidstone boundary value problems. Electron J Differ Equ 2(2000):1\u20138","journal-title":"Electron J Differ Equ"},{"key":"4732_CR11","doi-asserted-by":"publisher","first-page":"687","DOI":"10.1016\/S0895-7177(00)00165-5","volume":"32","author":"P Eloe","year":"2000","unstructured":"Eloe P, Henderson J, Thompson H (2000) Extremal points for impulsive Lidstone boundary value problems. Math Comput Model 32:687\u2013698","journal-title":"Math Comput Model"},{"key":"4732_CR12","doi-asserted-by":"publisher","first-page":"e1519","DOI":"10.1016\/j.na.2009.01.193","volume":"71","author":"J Fialho","year":"2009","unstructured":"Fialho J, Minh\u00f3s F (2009) Existence and location results for hinged beams with unbounded nonlinearities. Nonlinear Anal 71:e1519\u2013e1525","journal-title":"Nonlinear Anal"},{"key":"4732_CR13","first-page":"217","volume":"2013","author":"J Fialho","year":"2013","unstructured":"Fialho J, Minh\u00f3s F (2013) The role of lower and upper solutions in the generalization of Lidstone problems. Discrete Contin Dyn Syst Suppl 2013:217\u2013226","journal-title":"Discrete Contin Dyn Syst Suppl"},{"key":"4732_CR14","doi-asserted-by":"publisher","first-page":"271","DOI":"10.11650\/twjm\/1500407628","volume":"8","author":"Y Guo","year":"2004","unstructured":"Guo Y, Ge W (2004) Twin positive symmetric solutions for Lidstone boundary value problems. Taiwan J Math 8:271\u2013283","journal-title":"Taiwan J Math"},{"key":"4732_CR15","doi-asserted-by":"publisher","first-page":"22","DOI":"10.1016\/j.ijmecsci.2012.10.005","volume":"66","author":"TS Jang","year":"2013","unstructured":"Jang TS (2013) A new semi-analytical approach to large deflections of Bernoulli\u2013Euler-v.Karman beams on a linear elastic foundation: nonlinear analysis of infinite beams. Int J Mech Sci 66:22\u201332","journal-title":"Int J Mech Sci"},{"issue":"1","key":"4732_CR16","doi-asserted-by":"publisher","first-page":"339","DOI":"10.1016\/j.ijnonlinmec.2010.09.017","volume":"46","author":"TS Jang","year":"2011","unstructured":"Jang TS, Baek HS, Paik JK (2011) A new method for the nonlinear deflection analysis of an infinite beam resting on a nonlinear elastic foundation. Int J Non-Linear Mech. 46(1):339\u2013366","journal-title":"Int J Non-Linear Mech."},{"issue":"1","key":"4732_CR17","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1515\/dema-2015-0005","volume":"XLVIII","author":"M Jurkiewicz","year":"2015","unstructured":"Jurkiewicz M, Przeradzki B (2015) Existence of solutions for higher order BVP with paprameters via critical point theory. Demonstr Math XLVIII(1):53\u201361","journal-title":"Demonstr Math"},{"key":"4732_CR18","doi-asserted-by":"publisher","first-page":"537","DOI":"10.1137\/1032120","volume":"32","author":"AC Lazer","year":"1990","unstructured":"Lazer AC, Mckenna PJ (1990) Large-amplitude periodic oscillations in suspension bridges: some new connections with nonlinear analysis. SIAM Rev 32:537\u2013578","journal-title":"SIAM Rev"},{"key":"4732_CR19","doi-asserted-by":"publisher","first-page":"16","DOI":"10.1017\/S0013091500007501","volume":"2","author":"GJ Lidstone","year":"1929","unstructured":"Lidstone GJ (1929) Notes on the extension of Aitken\u2019s theorem (for polynomial interpolation) to the Everett types. Proc Edinb Math Soc 2:16\u201319","journal-title":"Proc Edinb Math Soc"},{"key":"4732_CR20","doi-asserted-by":"publisher","first-page":"97","DOI":"10.1016\/j.jmaa.2005.03.059","volume":"314","author":"Y Ma","year":"2006","unstructured":"Ma Y (2006) Existence of positive solutions of Lidstone boundary value problems. J Math Anal Appl 314:97\u2013108","journal-title":"J Math Anal Appl"},{"issue":"135","key":"4732_CR21","doi-asserted-by":"publisher","first-page":"161","DOI":"10.1007\/s10587-010-0006-6","volume":"60","author":"R Ma","year":"2010","unstructured":"Ma R, An Y (2010) Global structure of positive solutions for superlinear 2nth-boundary value problems. Czechoslov Math J 60(135):161\u2013172","journal-title":"Czechoslov Math J"},{"issue":"1","key":"4732_CR22","doi-asserted-by":"publisher","first-page":"114","DOI":"10.1016\/j.sandf.2012.01.004","volume":"52","author":"P Maheshwari","year":"2012","unstructured":"Maheshwari P, Khatri S (2012) Nonlinear analysis of infinite beams on granular bed-stone column-reinforced earth beds under moving loads. Soils Found 52(1):114\u2013125","journal-title":"Soils Found"},{"key":"4732_CR23","doi-asserted-by":"publisher","first-page":"1148","DOI":"10.1016\/j.jsv.2005.07.031","volume":"291","author":"AK Mallik","year":"2006","unstructured":"Mallik AK, Chandra S, Sarvesh S, Avinash B (2006) Steady-state response of an elastically supported infinite beam to a moving load. J Sound Vib 291:1148\u20131169","journal-title":"J Sound Vib"},{"key":"4732_CR24","doi-asserted-by":"crossref","first-page":"22","DOI":"10.3390\/axioms8010022","volume":"8","author":"F Minh\u00f3s","year":"2019","unstructured":"Minh\u00f3s F (2019) Heteroclinic solutions for classical and singular $$\\phi $$-Laplacian non-autonomous differential equations. Axioms 8:22","journal-title":"Axioms"},{"key":"4732_CR25","doi-asserted-by":"publisher","first-page":"1414","DOI":"10.1016\/j.jde.2018.07.072","volume":"266","author":"F Minh\u00f3s","year":"2019","unstructured":"Minh\u00f3s F, de Sousa R (2019) Existence of homoclinic solutions for second order coupled systems. J Differ Equ 266:1414\u20131428","journal-title":"J Differ Equ"},{"issue":"suppl.","key":"4732_CR26","first-page":"662","volume":"2005","author":"F Minh\u00f3s","year":"2005","unstructured":"Minh\u00f3s F, Gyulov T, Santos AI (2005) Existence and location result for a fourth order boundary value problem. Discrete Contin Dyn Syst 2005(suppl.):662\u2013671","journal-title":"Discrete Contin Dyn Syst"},{"issue":"4","key":"4732_CR27","doi-asserted-by":"publisher","first-page":"99","DOI":"10.3208\/sandf.45.4_99","volume":"45","author":"Y Momoya","year":"2005","unstructured":"Momoya Y, Etsuo S, Tatsuoka F (2005) Deformation characteristics of railway roadbed and subgrade under moving-wheel load. Soils Found 45(4):99\u2013118","journal-title":"Soils Found"},{"key":"4732_CR28","doi-asserted-by":"publisher","first-page":"103","DOI":"10.4064\/ap-56-2-103-121","volume":"2","author":"B Przeradzki","year":"1992","unstructured":"Przeradzki B (1992) The existence of bounded solutions for differential equations in Hilbert spaces. Ann Pol Math LVI 2:103\u2013121","journal-title":"Ann Pol Math LVI"},{"key":"4732_CR29","doi-asserted-by":"publisher","first-page":"78","DOI":"10.1006\/jdeq.2001.4135","volume":"184","author":"D Smets","year":"2002","unstructured":"Smets D, van den Berg JB (2002) Homoclinic solutions for Swift\u2013Hohenberg and suspension bridge type equations. J Differ Equ 184:78\u201396","journal-title":"J Differ Equ"},{"key":"4732_CR30","doi-asserted-by":"publisher","first-page":"65","DOI":"10.1016\/j.jmaa.2016.03.017","volume":"440","author":"R Vrabel","year":"2016","unstructured":"Vrabel R (2016) Formation of boundary layers for singularly perturbed fourth-order ordinary differential equations with the Lidstone boundary conditions. J Math Anal Appl 440:65\u201373","journal-title":"J Math Anal Appl"},{"key":"4732_CR31","doi-asserted-by":"publisher","first-page":"314","DOI":"10.1016\/j.jmaa.2005.01.019","volume":"308","author":"Y-M Wang","year":"2005","unstructured":"Wang Y-M (2005) Higher-order Lidstone boundary value problems for elliptic partial differential equations. J Math Anal Appl 308:314\u2013333","journal-title":"J Math Anal Appl"},{"key":"4732_CR32","doi-asserted-by":"publisher","first-page":"125","DOI":"10.1186\/1687-2770-2014-125","volume":"2014","author":"PJY Wong","year":"2014","unstructured":"Wong PJY (2014) Triple solutions of complementary Lidstone boundary value problems via fixed point theorems. Bound Value Probl 2014:125","journal-title":"Bound Value Probl"},{"key":"4732_CR33","first-page":"477","volume":"137","author":"Q Yao","year":"2003","unstructured":"Yao Q (2003) On the positive solutions of Lidstone boundary value problems. Appl Math Comput 137:477\u2013485","journal-title":"Appl Math Comput"},{"key":"4732_CR34","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-4838-5","volume-title":"Nonlinear functional analysis and its applications, I: fixed-point theorems","author":"E Zeidler","year":"1986","unstructured":"Zeidler E (1986) Nonlinear functional analysis and its applications, I: fixed-point theorems. Springer, New York"}],"container-title":["Neural Computing and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00521-020-04732-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00521-020-04732-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00521-020-04732-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,7,30]],"date-time":"2024-07-30T17:24:18Z","timestamp":1722360258000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00521-020-04732-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,1,24]]},"references-count":34,"journal-issue":{"issue":"16","published-print":{"date-parts":[[2020,8]]}},"alternative-id":["4732"],"URL":"https:\/\/doi.org\/10.1007\/s00521-020-04732-x","relation":{},"ISSN":["0941-0643","1433-3058"],"issn-type":[{"type":"print","value":"0941-0643"},{"type":"electronic","value":"1433-3058"}],"subject":[],"published":{"date-parts":[[2020,1,24]]},"assertion":[{"value":"18 July 2019","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"8 January 2020","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"24 January 2020","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Compliance with ethical standards"}},{"value":"The authors declare that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}