arXiv subjects

Mustapha Ait Hammou

Publications and source records attributed to Mustapha Ait Hammou.

3 recordsLinked to original sources

arXiv2021

Existence and uniqueness of solutions for a nonlinear equation with convection term

In this paper, we consider the existence and uniqueness of weak solutions of a nonlinear elliptic equation with a variable exponent, a monotonic type operator and a convection term. With the topological degree theory, we prove the existence of at least one weak solution under some Leray-Lions and growth conditions. Moreover, we obtain the uniqueness of the solution of the problem under some additional assumptions. Our results generalize and improve existing results with another approach.

math.AP↗

arXiv2019

Nonlinear problem involving the fractional p(x)-Laplacian operator by Topological degree

This paper is concerned with the study of a nonlinear problems involving the fractional p(x)-Laplacian operator. By means of the Berkovits degree theory, we prove the existence of nontrivial weak solutions for this problem. The appropriate functional framework for this problems is the fractional Sobolev spaces with variable exponent.

math.AP↗

arXiv2019

Dirichlet boundary value problem related to the $p(x)-$Laplacian with discontinuous nonlinearity

In this paper, we prove the existence of a weak solution for the Dirichlet boundary value problem related to the $p(x)-$Laplacian $$ -\mbox{div}(|\nabla u|^{p(x)-2}\nabla u)+u\in -[\underline{g}(x,u),\overline{g}(x,u)], $$ by using the degree theory after turning the problem into a Hammerstein equation. The right hand side $g$ is a possibly discontinuous function in the second variable satisfying some non-standard growth conditions..

math.AP↗