Multiplicity results for (p,q) fractional elliptic equations involving critical nonlinearities

Abstract

In this paper, we prove the existence of infinitely many nontrivial solutions for the class of (p, q) fractional elliptic equations involving concave-critical nonlinearities in bounded domains in R-N. Further, when the nonlinearity is of convex-critical type, we establish the multiplicity of nonnegative solutions using variational methods. In particular, we show the existence of at least cat(Omega)(Omega) nonnegative solutions.