GROUND STATE SOLUTIONS FOR SEMILINEAR PROBLEMS WITH A SOBOLEV-HARDY TERM

In this article, we study the existence of solutions to the problem -Delta u = gimel u + vertical bar u vertical bar(2)(s)*-(2)(u)/vertical bar y vertical bar(s), x is an element of Omega, u = 0, x is an element of partial derivative Omega, where Omega is a smooth bounded domain in R-N (N >= 3). We show that there is a ground state solution provided that N = 4 and gimel(m) < gimel <gimel(m vertical bar 1), or that N >= 5 and gimel(m) <= gimel < gimel(m+1), where gimel(m) is the m'th eigenvalue of -Delta with Dirichlet boundary conditions.