Existence result for double phase problem involving the $(p(x),q(x))$-Laplacian-like operators
نویسندگان
1 Laboratory LMACS, FST of Beni-Mellal, Sultan Moulay Slimane University, Morocco
2 Laboratory LMACS, FST of Beni-Mellal, Sultan Moulay Slimane University, Morocco
3 Laboratory LMACS, FST of Beni-Mellal, Sultan Moulay Slimane University, Morocco
4 Laboratory LMACS, FST of Beni-Mellal, Sultan Moulay Slimane University, Morocco
doi
10.22075/ijnaa.2023.28884.4014چکیده
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:\begin{equation*}\displaystyle\left\{\begin{array}{ll}\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,\end{array}\right.\end{equation*}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.
