Mountain pass solutions to semilinear problems with critical nonlinearity
Résumé
The mountain pass statement for semilinear elliptic equations $-\Delta u=f(u)$ in $\Bbb R^N$, $N>2$, with a critical exponent nonlinearity, namely $C_1\leq f(s)s/|s|^{2^*}\leq C_2$, satisfies the $({\rm PS})_c$ condition provided that the critical sequences are bounded and that the nonlinearity either has log-periodic oscillations or dominates its asymptotic values (relative to $|s|^{2^*}$) at zero and at infinity.