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 363
Ground state solutions for a nonlocal system in Fractional Orlicz-Sobolev Spaces
Hamza El-Houari, Lalla Saâdia Chadli, Hicham Moussa
Academic Editor: Youssef EL FOUTAYENI
Received
Accepted
Published
January 31, 2022
March 03, 2309
April 15, 2309

Abstract: In this document, we consider an elliptic problem type system involving by the non-local fractional $a(.)$-Laplacian operator defined by J. F Bonder et A. M. Salort in [1], with boundary conditions type Dirichlet, where $a(.)$ is an Orlizc function ( we refer to [2] and [3] for more detail). By using the minimization arguments on suitable Nehari manifolds, we get a ground state solution. The main difficulty in this work arises from the complicated method which we are applying to find the solution, Furthermore the inhomogeneities of the fractional $a(.)$-Laplacian operator.