American Institute of Mathematical Sciences

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

Mountain pass solutions to semilinear problems with critical nonlinearity

Ian Schindler 1, and  Kyril Tintarev 2,

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.
Keywords: critical exponent, Talenti solution, Semilinear elliptic equations, concentration compactness..
Mathematics Subject Classification: Primary 35J20, 35J6.
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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