@article {
author = {Soukaina, Yacini and El Ouaarabi, Mohamed and Chakir, Allalou and Khalid, Hilal},
title = {Existence result for double phase problem involving the $(p(x),q(x))$-Laplacian-like operators},
journal = {International Journal of Nonlinear Analysis and Applications},
volume = {14},
number = {1},
pages = {3201-3210},
year = {2023},
publisher = {Semnan University},
issn = {2008-6822},
eissn = {2008-6822},
doi = {10.22075/ijnaa.2023.28884.4014},
abstract = {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.},
keywords = {Dirichlet problems,double phase problems,(p(x),q(x))- Laplacian-like operators,topological degree methods},
url = {https://ijnaa.semnan.ac.ir/article_7394.html},
eprint = {https://ijnaa.semnan.ac.ir/article_7394_ac48226139d56c56eda4f97c2079f4fb.pdf}
}