On positive weak solutions for a class of weighted (p(.), q(.))−Laplacian systems

Abstract

In this paper, we study the existence of positive weak solutions for a quasilinear elliptic system involving weighted (p(.), q(.))−Laplacian operators. The approach is based on sub-supersolutions method and on Schauder’s fixed point theorem.

Leray-Schauder’s solution for a nonlocal problem in a fractional Orlicz-Sobolev space

“…For the problems involving fractional p−Laplace operator, we refer the reader to the works [8,9,10,11]. they use different methods to establish the existence of solutions.…”

Three solutions for fractional $p(x,.)$-Laplacian Dirichlet problems with weight

“…is a continuous function, possesses more complicated properties than the p-Laplacian operator mainly due to the fact that it is not homogeneous. There has been many results devoted to the existence of solutions for variable exponent problems; see, e.g., [4,5,6] and the references therein. More recently, some researchers extended the integer case to the fractional one.…”