Existence and multiplicity solutions for a singular elliptic p(x)-Laplacian equation
Main Article Content
Abstract
This paper deals with the existence and multiplicity of nontrivial weak solutions for the following equation
involving variable exponents:
\begin{align*}
\begin{cases}
-\vartriangle_{p(x)}u+\dfrac{\vert u\vert^{r-2}u}{|x|^{r}}=\lambda h(x,u),&in ~\Omega,\\
u=0,&on~\partial\Omega,
\end{cases}
\end{align*}
where $\Omega$ is a bounded domain of $\mathbb{R}^{N}$ with smooth enough boundary which is subject to Dirichlet boundary condition.
Using a variational method and Krasnoselskii's genus theory, we would show the existence and
multiplicity of the solutions. Next, we study closedness of set of eigenfunctions, such that $p(x)\equiv p$.
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