Multiplicity of Positive Solutions for a Nonlocal Elliptic Problem Involving Critical Sobolev-Hardy Exponents and Concave-Convex Nonlinearities

In this article, we study the following critical problem involving the fractional Laplacian: {(-Δ)α2u−γu|x|α=λ|u|q−2|x|s+u2α*(t)-2u|x|tinΩ,u=0inRN\Ω, where Ω ⊂ ℝ^N (N > α) is a bounded smooth domain containing the origin, α ∈ (0,2), 0 ≤ s, t < α, 1 ≤ q < 2, λ > 0, 2α*(t)=2(N-t)N-α is the fractional critical Sobolev-Hardy exponent, 0 ≤ γ < γ_H, and γ_H is the sharp constant of the Sobolev-Hardy inequality. We deal with the existence of multiple solutions for the above problem by means of variational methods and analytic techniques.