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: {(-Delta)alpha 2u-gamma u|x|alpha=lambda|u|q-2|x|s+u2 alpha*(t)-2u|x|tin omega,u=0inRN\omega, where omega subset of Double-struck capital R-N (N > alpha) is a bounded smooth domain containing the origin, alpha is an element of (0,2), 0 <= s, t < alpha, 1 <= q < 2, lambda > 0, 2 alpha*(t)=2(N-t)N-alpha is the fractional critical Sobolev-Hardy exponent, 0 <= gamma < gamma(H), and gamma(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.