A concentration-compactness lemma with applications to singular eigenvalue problems

Let Omega subset of or equal to R-N be any open set. We study the nonlinear eigenvalue problem - Delta(p)u = lambda V(x) u(p-2) u, u epsilon D-0(1,p)(Omega) where 1 < p < N and V is an element of L-loc(1)(Omega) may have strong singularities and an indefinite sign. The key ingredient is a precised concentration-compactness lemma related to V-dependent limiting problems. This work follows, extends, and simplifies that of A. Tertikas (1998, J. Funct. Anal. 154, 42-66) dealing with the positive linear case for Omega = R-N. (C) 1999 Academic Press