On a fractional (p,q) -Laplacian equation with critical nonlinearities

In this paper, we consider the following fractional (p,q)-Laplacian equations with critical Hardy-Sobolev exponents {(−Δ)ps1u+(−Δ)qs2u=λ|u|r−2u+μ|u|ps1∗(α)−2u|x|αinΩ,u=0inRN∖Ω, where 00 are two parameters, 0≤α<ps1 and ps1∗(α)=p(N−α)N−ps1 is the fractional Hardy-Sobolev critical exponent, Ω⊂RN is an open bounded domain with smooth boundary. By using variational methods, we show that the problem has a nontrivial nonnegative weak solution.