INFINITELY MANY SIGN-CHANGING SOLUTIONS FOR THE HARDY-SOBOLEV-MAZ'YA EQUATION INVOLVING CRITICAL GROWTH

In this paper, we consider the existence of infinitely many sign-changing solutions for the following Hardy-Sobolev-Maz'ya equation {-Delta u - mu u/vertical bar y vertical bar(2) = lambda u + vertical bar u vertical bar(2)*((t)) (- 2)u/vertical bar y vertical bar(t) in Omega u = 0 on partial derivative Omega, where Omega is an open bounded domain in R-N, R-N = R-k x RN - k , lambda > 0, 0 <= mu < (k- 2)(2) / 4 when k > 2, mu = 0 when k = 2 and 2*(t) = 2(N- t) / (N- 2). A point x is an element of R-N is denoted as x (y , z) is an element of R-k x RN - k, and the points x(0) = (0,z(0)) are contained in Omega. By using a compactness result obtained in [39], we prove the existence of infinitely many sign changing solutions by a combination of the invariant sets method and the Ljusternik-Schnirelman type minimax method.