Existence of positive solutions of elliptic equations with Hardy term

This paper is devoted to studying the existence of positive solutions of the problem: {-Delta u = u(p)/vertical bar x vertical bar(a) + h(x, u, del u), in Omega u = 0, on partial derivative Omega (*) where Omega subset of R-N(N >= 3) is an open bounded smooth domain with boundary partial derivative Omega, and 1 < p < N-a/N-2, 0 < a < 2. Under suitable conditions of h(x, u, del u), we get a priori estimates for the positive solutions of problem (*). By making use of these estimates and topological degree theory, we further obtain some existence results for the positive solutions of problem (*) when 1 < p < N-a/N-2.