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Homotopy and nonlinear boundary value problems involving singular \({\phi}\)-Laplacians

  • Jean Mawhin
Article

Abstract

Homotopy methods are used to find sufficient conditions for the solvability of nonlinear boundary value problems of the form
$$(\phi(u^\prime))^\prime = f(t, u, u^\prime), \quad g(u(\alpha), \phi(u^\prime(\beta))) = 0,$$
where (α, β) = (0, 1), (1, 0), (0, 0) or (1, 1), \({\phi}\) is a homeomorphism from the open ball \({B(a) \subset \mathbb{R}^n}\) onto \({\mathbb{R}^n}\), f is a Carathéodory function, \({g : \mathbb{R}^n \times \, \mathbb{R}^n \rightarrow \mathbb{R}^m}\) is continuous and m ≤ 2n.

Mathematics Subject Classification

34B15 34B16 47H11 55Q45 

Keywords

Singular \({\phi}\)-Laplacian nonlinear boundary value problem degree stable homotopy Hopf map 

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Copyright information

© Springer Basel 2013

Authors and Affiliations

  1. 1.Institut de Recherche en Mathématique et PhysiqueUniversité Catholique de LouvainLouvain-la-NeuveBelgium

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