@ARTICLE{10.21494/ISTE.OP.2022.0840, TITLE={Existence Results for Singular p(x)-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://www.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 $$\left\{ \begin{array}{ll} \Delta\Big(｜x｜^{p(x)}｜\Delta u｜^{p(x)-2}\Delta u\Big)=a(x)u^{-\gamma (x)}+\lambda f(x,u),\quad \mbox{in }\Omega, \\ u=\Delta u=0, \quad \mbox{on }\partial\Omega. \end{array} \right.$$$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.}}