Concentration-compactness principle and applications to nonlocal elliptic problems.

Abstract

The main goal of this work is to analyze concentration-compactness principles for fractional Sobolev spaces based on the concentrationcompactness principle of P.-L. Lions and in the profile decomposition for weak convergence in Hilbert spaces due to K. Tintarev and K.-H Fieseler. As application, we address questions on compactness of the associated energy functional to some nonlocal elliptic problems. We obtain existence results for a wide class of possible singular potentials not necessarily bounded away from zero and for oscillatory nonlinearities in both subcritical and critical growth range that may not satisfy the Ambrosetti-Rabinowitz condition.