In this article, we extend the well-known concentration - compactness principle by Lions to the variable exponent case. We also give some applications to the existence problem for the p(x)-Laplacian with critical growth.

In this paper we extend the well-known concentration-compactness principle for the Fractional Laplacian operator in unbounded domains. As an application we show sufficient conditions for the existence of solutions to some ...

The main goal of this work is to prove the existence of three different solutions (one positive, one negative and one with nonconstant sign) for the equation (−Δp)su=|u|ps ⁎−2u+λf(x,u) in a bounded domain with Dirichlet ...

In this paper we study sufficient local conditions for the existence of non-trivial solution to a critical equation for the p(x)-Laplacian where the critical term is placed as a source through the boundary of the domain. ...

We prove a general result about the behaviour of minimizing sequences for nonlocal shape functionals satisfying suitable structural assumptions. Typical examples include functions of the eigenvalues of the fractional ...