Weighted Steklov problem under nonresonance conditions
| Autor: | Aboubacar Marcos, Jonas Têlé Doumatè |
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| Rok vydání: | 2018 |
| Předmět: | |
| Zdroj: | Boletim da Sociedade Paranaense de Matemática, Vol 36, Iss 4, Pp 87-105 (2018) |
| ISSN: | 2175-1188 0037-8712 |
| Popis: | We deal with the existence of weak solutions of the nonlinear problem $-\Delta_{p}u+V|u|^{p-2}u$ in a bounded smooth domain $\Omega\subset \mathbb{R}^{N}$ which is subject to the boundary condition $|\nabla u|^{p-2}\frac{\partial u}{\partial \nu}=f(x,u)$. Here $V\in L^{\infty}(\Omega)$ possibly exhibit both signs which leads to an extension of particular cases in literature and $f$ is a Carathéodory function that satisfies some additional conditions. Finally we prove, under and between nonresonance condtions, existence results for the problem. |
| Databáze: | OpenAIRE |
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