  In the paper we show that critical sequences associated with the mountain
pass level for semilinear elliptic problems on $\R^N$ 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.

Analysis of PDEs;Functional Analysis