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# Article

 Title: Existence of multiple solutions for a third-order three-point regular boundary value problem (English) Author: Šenkyřík, Martin Language: English Journal: Mathematica Bohemica ISSN: 0862-7959 (print) ISSN: 2464-7136 (online) Volume: 119 Issue: 2 Year: 1994 Pages: 113-121 Summary lang: English . Category: math . Summary: In the paper we prove an Ambrosetti-Prodi type result for solutions $u$ of the third-order nonlinear differential equation, satisfying $u'(0)=u'(1)=u(\eta)=0,\ 0\leq\eta \leq 1$. (English) Keyword: boundary value problem Keyword: lower and upper solutions Keyword: degree theory Keyword: Ambrosetti-Prodi type theorem Keyword: coincidence degree Keyword: Nagumo functions Keyword: Ambrosetti-Prodi results MSC: 34B10 MSC: 34B15 idZBL: Zbl 0805.34018 idMR: MR1293243 DOI: 10.21136/MB.1994.126080 . Date available: 2009-09-24T21:03:45Z Last updated: 2020-07-29 Stable URL: http://hdl.handle.net/10338.dmlcz/126080 . Reference: [1] A. Ambrosetti, G. Prodi: On the inversion of some differentiate mappings with singularities between Banach spaces.Ann. Mat. Pura Appl. 93 (4) (1972), 231-247. MR 0320844, 10.1007/BF02412022 Reference: [2] S. H. Ding, J. Mawhin: A multiplicity result for periodic solutions of higher order ordinary differential equations.Differential and Integral Equations 1(1). Zbl 0715.34086, MR 0920487 Reference: [3] C. Fabry J. Mawhin, M. Nkashama: A multiplicity result for periodic solutions of forced nonlinear second order ordinary differential equations.Bull. London Math. Soc. 18 (1986), 173-180. MR 0818822, 10.1112/blms/18.2.173 Reference: [4] J. Mawhin: Topological degree methods in nonlinear boundary value problems.CBMS Regional Confer. Ser. Math. No. 40. Amer. Math. Soc., Providence, 1979. Zbl 0414.34025, MR 0525202, 10.1090/cbms/040 Reference: [5] J. Mawhin: First order ordinary differential equations with several solutions.Z. Angew. Math. Phys. 38 (1987), 257-265. MR 0885688, 10.1007/BF00945410 Reference: [6] M. Šenkyřík: Method of lower and upper solutions for a third-order three-point regular boundary value problem.Acta Univ. Palack. Olomouc. Fac. Rerum Natur. Math. XXXI (1992), 60-70. MR 1212606 .

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