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Article

Keywords:
boundary value problem; lower and upper solutions; degree theory; Ambrosetti-Prodi type theorem; coincidence degree; Nagumo functions; Ambrosetti-Prodi results
Summary:
In the paper we prove an Ambrosetti-Prodi type result for solutions $u$ of the third-order nonlinear differential equation, satisfying $u'(0)=u'(1)=u(\eta)=0,\ 0\leq\eta \leq 1$.
References:
[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. DOI 10.1007/BF02412022 | MR 0320844
[2] S. H. Ding, J. Mawhin: A multiplicity result for periodic solutions of higher order ordinary differential equations. Differential and Integral Equations 1(1). MR 0920487 | Zbl 0715.34086
[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. DOI 10.1112/blms/18.2.173 | MR 0818822
[4] J. Mawhin: Topological degree methods in nonlinear boundary value problems. CBMS Regional Confer. Ser. Math. No. 40. Amer. Math. Soc., Providence, 1979. MR 0525202 | Zbl 0414.34025
[5] J. Mawhin: First order ordinary differential equations with several solutions. Z. Angew. Math. Phys. 38 (1987), 257-265. DOI 10.1007/BF00945410 | MR 0885688
[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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