# American Institute of Mathematical Sciences

2007, 2007(Special): 912-919. doi: 10.3934/proc.2007.2007.912

## Mountain pass solutions to semilinear problems with critical nonlinearity

 1 Université des Sciences Sociales-UT1-Manufacture des Tabacs, 21 alles de Brienne, 31000 Toulouse, France 2 Department of Mathematics, Uppsala University, P.O. Box 480, 751 06 Uppsala, Sweden

Received  September 2006 Revised  April 2007 Published  September 2007

The mountain pass statement for semilinear elliptic equations −$\Deltau = f(u)$ in $\mathbb{R}^N, N > 2$, with a critical exponent nonlinearity, namely $C_1 <= f(s)s/|s|^2^* <= C_2$, satisfies the (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.
Citation: Ian Schindler, Kyril Tintarev. Mountain pass solutions to semilinear problems with critical nonlinearity. Conference Publications, 2007, 2007 (Special) : 912-919. doi: 10.3934/proc.2007.2007.912
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