| Autor: |
Aboubacar Abdou, Aboubacar Marcos |
| Jazyk: |
angličtina |
| Rok vydání: |
2016 |
| Předmět: |
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| Zdroj: |
Electronic Journal of Differential Equations, Vol 2016, Iss 197,, Pp 1-19 (2016) |
| Druh dokumentu: |
article |
| ISSN: |
1072-6691 |
| Popis: |
In this article we study the existence of solutions for the Dirichlet problem $$\displaylines{ -\text{div}(| \nabla u |^{p(x)-2}\nabla u)+V(x)|u|^{q(x)-2}u =f(x,u)\quad \text{in }\Omega,\cr u=0\quad \text{on }\partial \Omega, }$$ where $\Omega$ is a smooth bounded domain in $\mathbb{R}^N$, V is a given function in a generalized Lebesgue space $L^{s(x)}(\Omega)$ and f(x,u) is a Caratheodory function which satisfies some growth condition. Using variational arguments based on "Fountain theorem" and "Dual Fountain theorem", we shall prove under appropriate conditions on the above nonhomogeneous quasilinear problem the existence of two sequences of weak solutions for this problem. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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