Research Communication | Open Access
Volume 2021 | Communication ID 127
Volume 2021 | Communication ID 127
| Existence Results For Some Nonlinear Elliptic Equations Via Topological Degree Methods |
Abderrazak Kassidi, Adil Abbassi, Chakir Allalou
Received |
Accepted |
Published |
January 28, 2021 |
February 15, 2021 |
March 15, 2021 |
Abstract: This article is devoted to study the existence of weak solutions to a Dirichlet boundary value problem related to the following nonlinear elliptic equation: -div(a(x,u,\nabla u))-\lambda\ g(x,u,\nabla u)=b(x){|u|}^{q-2}u, where -div(a(x,u,\nabla\ u)) is a Leray-Lions operator acting from W_0^{1,p}(Ω,w) to its dual W_0^{-1,p'}(Ω,w*). On the nonlinear term g\left(x,s,\eta\right), we only assume the growth condition on \eta. Our approach is based on the topological degree introduced by Berkovits.