Titre : Existence Results for Singular <em>p</em>(<em>x</em>)-Laplacian Equation 

Auteurs : R. Alsaedi, K. Ben Ali, A. Ghanmi,  

Revue : Advances in Pure and Applied Mathematics 

Numéro : Issue 3 (June 2022) 

Volume : 13 

Date : 2022/06/1 

DOI : 10.21494/ISTE.OP.2022.0840 

ISSN : 1869-6090 

Résumé : This paper is concerned with the existence of solutions for the following class of singular fourth order elliptic equations
$$$
\left\{
 \begin{array}{ll}
 \Delta\Big(&#xFF5C;x&#xFF5C;^{p(x)}&#xFF5C;\Delta u&#xFF5C;^{p(x)-2}\Delta u\Big)=a(x)u^{-\gamma (x)}+\lambda f(x,u),\quad \mbox{in }\Omega, \\
 u=\Delta u=0,  \quad \mbox{on }\partial\Omega.
 \end{array}
 \right.$$$
where $$$\Omega$$$ is a smooth bounded domain in $$$\mathbb{R}^N, \gamma :\overline{\Omega}\rightarrow (0,1)$$$ be a continuous function, $$$f\in C^{1}( \overline{\Omega}\times \mathbb{R}),  p:\; \overline{\Omega}\longrightarrow \;(1,\infty)$$$ and $$$a$$$ is a function that is almost everywhere positive in $$$\Omega$$$. Using variational techniques combined with the theory of the generalized Lebesgue-Sobolev spaces, we prove the existence at least one nontrivial weak solution. 

Éditeur : ISTE OpenScience