Existence result for double phase problem involving the $(p(x),q(x))$-Laplacian-like operators | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 250، دوره 14، شماره 1، فروردین 2023، صفحه 3201-3210 اصل مقاله (405.74 K) | ||
| نوع مقاله: Review articles | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2023.28884.4014 | ||
| نویسندگان | ||
| Yacini Soukaina* 1؛ Mohamed El Ouaarabi2؛ Allalou Chakir2؛ Hilal Khalid2 | ||
| 1Laboratory LMACS, FST of Beni-Mellal, Sultan Moulay Slimane University, Morocco | ||
| 2Laboratory LMACS, FST of Beni-Mellal, Sultan Moulay Slimane University, Morocco | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Dirichlet problems؛ double phase problems؛ (p(x),q(x))- Laplacian-like operators؛ topological degree methods | ||
| مراجع | ||
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