Critical fractional elliptic equations with exponential growth

摘要

In this paper we establish, using variational methods combined with the Moser-Trudinger inequality, existence and multiplicity of weak solutions for a class of critical fractional elliptic equations with exponential growth without a Ambrosetti-Rabinowitz-type condition. The interaction of the nonlinearities with the spectrum of the fractional operator will be used to study the existence and multiplicity of solutions. The main technical result proves that a local minimum in C-s(0)((Omega) over bar )is also a local minimum in W-0(s,p) for exponentially growing nonlinearities.