Positive Solutions for Perturbed Fractional p-Laplacian Problems

Abstract

In this article, we consider a class of quasilinear elliptic equations involving the fractional p-Laplacian, in which the nonlinear term satisfies subcritical or critical growth. Based on a fixed point result due to Carl and Heikkilä, we can well overcome the lack of compactness which has been a key difficulty for elliptic equations with critical growth. Moreover, we establish the existence and boundedness of the weak solutions for the above equations.