In this paper, the following problem is considered: {-Delta(p)u - mu vertical bar u vertical bar(p-2)u vertical bar x vertical bar(p) = lambda f (x)vertical bar u vertical bar(q-2)u + g(x)vertical bar u vertical bar(p)*(-2)u, x is an element of Omega, u = 0, x is an element of Omega, where Omega subset of R(N) is a bounded domain such that 0 is an element of Omega, 1 < q < p, lambda > 0, mu < , f and g are nonnegative functions, (mu) over bar = (N-p/p)(p) is the best Hardy constant and p* = Np/N-p is the critical Sobolev exponent. By extracting the Palais-Smale sequence in the Nehari manifold,...
