Multiplicity of solutions for an elliptic problem with critical sobolev-hardy exponents and concave-convex nonlinearities

We study the existence of multiple solutions for the following elliptic problem: - δ p u - | u | p - 2 u / | x | p = | u | p * (t) - 2 / | x | t u + | u | q - 2 / | x | s u,u ∈ w 0 1,p (ω). we prove that if 1 ≤ q < p < n,then there is a μ 0,such that for any μ ∈ 0,μ 0,the above mentioned problem possesses infinitely many weak solutions. our result generalizes a similar result (azorero and alonso,1991). © 2014 juan li and yuxia tong.