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

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 $ca{t}_{\mathrm{\Omega }}(\mathrm{\Omega })$ nonnegative solutions.