Existence result for double phase problem involving the $(p(x),q(x))$-Laplacian-like operators

Document Type : Review articles


Laboratory LMACS, FST of Beni-Mellal, Sultan Moulay Slimane University, Morocco


The paper study the existence of at least one weak solutions for Dirichlet boundary value problem involving the $\big(p(x),q(x)\big)$-Laplacian-like operators of the following form:
\displaystyle-\Delta^{l}_{p(x)}-\Delta^{l}_{q(x)}=\lambda g(x, u, \nabla u) & \mathrm{i}\mathrm{n}\ \Omega,\\\\
u=0 & \mathrm{o}\mathrm{n}\ \partial\Omega,
where $\Delta^{l}_{r(x)} $ is the $r(x)$-Laplacian-like operators, $\Omega$ is a smooth bounded domain in $\mathbb{R}^{N}$, $\lambda$ is a real parameter and $g$ is Carath'eodory function satisfies the assumption of growth. The existence is proved by using Berkovits' topological degree.


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Volume 14, Issue 1
January 2023
Pages 3201-3210
  • Receive Date: 03 November 2022
  • Revise Date: 08 January 2023
  • Accept Date: 13 January 2023