Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

Nonlinear Problem Involving the Fractional P(x)-Laplacian Operator by Topological Degree

Author(s):

Ait Hammou Mustapha

Doctor of Applied Mathematics, Professor in the Department of Mathematics, Laboratory of Mathematical Analysis and Applications, Faculty of Sciences Dhar El Mahraz, Sidi Mohamed Ben Abdellah University, Fez, Morocco.

mustapha.aithammou@usmba.ac.ma

Abstract:

This paper is concerned with the study of a nonlinear problem 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 problem is the fractional Sobolev spaces with variable exponent.

Keywords

• Degree theory
• fractional p(x)-Laplacian operator
• fractional Sobolev spaces with variable exponent
• Nonlinear elliptic problem

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