Existence And Multiplicity Results For The Fractional P-laplace Equation With Hardy-Sobolev Exponents

In this paper,we investigate the following fractional p-Laplacian problem (?) where ? is a bounded domain containing the origin in RN with Lipschitz boundary,p ?(1,?),s ?(0,1),0 ??<ps<N and ps,?*=(N-?)p/(N-ps)is the fractional Hardy-Sobolev exponent.We prove the existence,multiplicity,and bifur-cation results for the above problem.Our results extend some results in the literature for the fractional p-Laplacian problem involving critical Sobolev exponent and the p-Laplacian problem involving Hardy-Sobolev exponents.