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Soukaina, Yacini, El Ouaarabi, Mohamed, Chakir, Allalou, Khalid, Hilal. (1401). Existence result for double phase problem involving the $(p(x),q(x))$-Laplacian-like operators. نشریه هنرهای کاربردی, 14(1), 3201-3210. doi: 10.22075/ijnaa.2023.28884.4014
Yacini Soukaina; Mohamed El Ouaarabi; Allalou Chakir; Hilal Khalid. "Existence result for double phase problem involving the $(p(x),q(x))$-Laplacian-like operators". نشریه هنرهای کاربردی, 14, 1, 1401, 3201-3210. doi: 10.22075/ijnaa.2023.28884.4014
Soukaina, Yacini, El Ouaarabi, Mohamed, Chakir, Allalou, Khalid, Hilal. (1401). 'Existence result for double phase problem involving the $(p(x),q(x))$-Laplacian-like operators', نشریه هنرهای کاربردی, 14(1), pp. 3201-3210. doi: 10.22075/ijnaa.2023.28884.4014
Soukaina, Yacini, El Ouaarabi, Mohamed, Chakir, Allalou, Khalid, Hilal. Existence result for double phase problem involving the $(p(x),q(x))$-Laplacian-like operators. نشریه هنرهای کاربردی, 1401; 14(1): 3201-3210. doi: 10.22075/ijnaa.2023.28884.4014

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
تاریخ دریافت: 12 آبان 1401،  تاریخ بازنگری: 18 دی 1401،  تاریخ پذیرش: 23 دی 1401 
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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