Fourth Edition of the International Conference on Research in Applied Mathematics and Computer Science ICRAMCS 2022
 March 24-25-26, 2022
Online and Face-to-Face Conference

ICRAMCS, 4 (2022) | Proceedings ISSN: 2605-7700

Research Communication | Open Access
Volume 2022 | Communication ID 384
Existence of Solution for p(x)− Kirchhoff- Type System
Abdesslam Ouaziz, Ahmed Aberqi
Academic Editor: Youssef EL FOUTAYENI
Received
Accepted
Published
January 31, 2022
March 03, 2326
April 15, 2326

Abstract: This paper is concerned with existence of solutions to a class of $p(x)-$ Kirchhoff of systems type: \begin{equation}\label{k1} \begin{dcases} M(A(x, \nabla u)) \operatorname{div}(a(x, \nabla u))=\frac{\partial F}{\partial u}(x, u, v) \text { in }\Omega, \\ M(A(x, \nabla v)) \operatorname{div}(a(x, \nabla v)) = \frac{\partial F}{\partial v}(x, u, v) \text { in } \Omega, \\ u=v=0 \quad \text { in } \mathbb{R}^{N} \backslash \Omega, \end{dcases} \end{equation} where $\Omega \subset\mathbb{R^{N}}, M\in C^{0}(\mathbb{R}), $ and $F\in C^{1}(\Omega \times \mathbb{R} \times \mathbb{R}, ...