Concentration-compactness principle for mountain pass problems

Abstract

In the paper we show that critical sequences associated with the mountain pass level for semilinear elliptic problems on ${\mathbb{R}}^N$ converge when the non-linearity is subcritical, superlinear and satisfies the penalty condition $F_{\infty }(s)<F(x,s)$. The proof suggests a concentration compactness framework for minimax problems, similar to that of P.-L.Lions for constrained minima.