Existence of Solutions for Fractional (p, q)-Laplacian Problems Involving Critical Hardy-Sob olev Nonlinearities

This paper is devoted to studying a class of fractional (p,q)-Laplacianproblems with subcritical and critical Hardy potentials: {(-triangle)(p)(s1)u+nu(-triangle)(q)(s2)u=lambda|u|(r-2)u/|x|(a)+|u|p(& lowast;s1)((b)-2)u in Omega x in R-N\ohm, where ohm subset of R(N )is a smooth and bounded domain, and p(s1)(b) =(N-b)/p/N-ps(1 )denotes the fractional critical Hardy-Sobolev exponent. More precisely, when nu= 1 and nu >0 is sufficiently small, using some asymptotic estimates and the Mountain Pass Theorem, we establish the existence results for the above fractional elliptic equation under some suitable hypotheses, respectively, which are gained over a wider range of parameters.