Existence of solutions for a fractional m&n-Laplacian system with Hardy-Sobolev exponents

Abstract In this article, our purpose is to study weak solutions for a fractional m&n-Laplacian system with Hardy-Sobolev critical exponents. It is hard to find a classical solution for our system, so we will discuss a weak solution for its energy function. We will also study the Sobolev spaces that can be used in compact embedding. With the help of some inequalities, we show that the sequence we used is bounded in our Sobolev spaces. Finally, we can prove that our system has a nontrivial solution.