Homotopy and nonlinear boundary value problems involving singular {\phi}-Laplacians |
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Authors: | Jean Mawhin |
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Institution: | 1. Institut de Recherche en Mathématique et Physique, Université Catholique de Louvain, B-1348, Louvain-la-Neuve, Belgium
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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. |
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