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: -Delta(p)u - mu(vertical bar u vertical bar(p-2)u/vertical bar x vertical bar(p)) = (vertical bar u vertical bar(p)*(t)-2/vertical bar x vertical bar t)u + lambda(vertical bar u vertical bar(q-2)/vertical bar x vertical bar(s))u, u epsilon W-0(1,p)(Omega). We prove that if 1 <= q < p < N, then there is a mu(0), such that for any mu epsilon (0,mu(0)), the above mentioned problem possesses infinitely many weak solutions. Our result generalizes a similar result (Azorero and Alonso, 1991).