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
Research Communication | Open Access
Volume 2022 | Communication ID 16
Volume 2022 | Communication ID 16
| Existence results for a class of Steklov problems with (p(x),q(x)-Laplacian |
Abdessamad Lakhdi, Belhaj Karim
Received |
Accepted |
Published |
October 24, 2021 |
March 03, 2032 |
April 15, 2032 |
Abstract: This work discusses the elliptic problem \begin{equation*} \left\{ \begin{array}{ll} -\triangle_{p(x)}u-\triangle_{q(x)}u=\lambda(x)f(x,u) & \text{in } \Omega, \\ \left(|\nabla u|^{p(x)-2}+|\nabla u|^{q(x)-2}\right)\frac{\partial u}{\partial\nu}+|u|^{p(x)-2}u+|u|^{q(x)-2}u=\mu(x)g(x,u) & \text{on } \partial\Omega, \end{array} \right. \end{equation*} where $\Omega\subset\mathbb{R}^N(N \geq 3)$ is a bounded domain with smooth boundary $\partial\Omega$ and $\nu$ is the unit outward normal vector on $\partial\Omega$. $p, \; q: \overline{\Omega} \mapsto (1,+\infty)$ are continuous functions such ...