Mountain pass solutions to semilinear problems with critical nonlinearity

Ian Schindler; Kyril Tintarev

doi:10.3934/proc.2007.2007.912

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2007, Volume 2007: 912-919. Doi: 10.3934/proc.2007.2007.912 open access

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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
2.
Department of Mathematics, Uppsala University, P.O. Box 480, 751 06 Uppsala

Received: September 2006

Revised: April 2007

Published: August 2007

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Abstract

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.

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Mathematics Subject Classification: Primary 35J20, 35J60.

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