TY  - Type of reference 
TI  - Résultats d&#8217;existence pour l&#8217;equation du <em>p</em>(<em>x</em>)-laplacien singulier 
AU  - R. Alsaedi 
AU  - K. Ben Ali 
AU  - A. Ghanmi 
AB  - 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. 
DO  - 10.21494/ISTE.OP.2022.0840 
JF  - Avancées en Mathématiques Pures et Appliquées 
KW  - p(x)-biharmonic,  variable exponent Lebesgue space,  variable exponent Sobolev space, p(x)-biharmonic,  variable exponent Lebesgue space,  variable exponent Sobolev space,  
L1  - https://www.openscience.fr/IMG/pdf/iste_apam22v13n3_4.pdf 
LA  - fr 
PB  - ISTE OpenScience 
DA  - 2022/06/1er 
SN  - 1869-6090 
TT  - Existence Results for Singular <em>p</em>(<em>x</em>)-Laplacian Equation 
UR  - https://www.openscience.fr/Resultats-d-existence-pour-l-equation-du-p-x-laplacien-singulier 
IS  - Numéro 3 (Juin 2022) 
VL  - 13 
ER  -