@ARTICLE{10.21494/ISTE.OP.2022.0840, 

TITLE={Existence Results for Singular <em>p</em>(<em>x</em>)-Laplacian Equation}, 
  
AUTHOR={R. Alsaedi, K. Ben Ali, A. Ghanmi, }, 
	
JOURNAL={Advances in Pure and Applied Mathematics}, 
	
VOLUME={13}, 

NUMBER={Issue 3 (June 2022)}, 
	
YEAR={2022}, 

URL={https://openscience.fr/Existence-Results-for-Singular-p-x-Laplacian-Equation}, 
	
DOI={10.21494/ISTE.OP.2022.0840}, 
	
ISSN={1869-6090}, 
	
ABSTRACT={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.}}