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 $cat_{\Omega}(\Omega)$ nonnegative solutions.