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 ${\mathbb{R}}^N$. 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 $ca{t}_{\Omega }(\Omega )$ nonnegative solutions.

36 pages

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