TY - Type of reference
TI - Résultats d’existence pour l’equation du p(x)-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
$$$
\left\{
\begin{array}{ll}
\Delta\Big(|x|^{p(x)}|\Delta u|^{p(x)-2}\Delta u\Big)=a(x)u^{-\gamma (x)}+\lambda f(x,u),\quad \mbox{in }\Omega, \\
u=\Delta u=0, \quad \mbox{on }\partial\Omega.
\end{array}
\right.$$$
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.
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 p(x)-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 -