Mountain pass solutions to semilinear problems with critical nonlinearity

Pages: 912 - 919, Issue Special, September 2007

 Abstract        Full Text (198.1K)              

Ian Schindler - Université des Sciences Sociales-UT1-Manufacture des Tabacs, 21 alles de Brienne, 31000 Toulouse, France (email)
Kyril Tintarev - Department of Mathematics, Uppsala University, P.O. Box 480, 751 06 Uppsala, Sweden (email)

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.

Keywords:  Semilinear elliptic equations, critical exponent, Talenti solution, concentration compactness.
Mathematics Subject Classification:  Primary 35J20, 35J60.

Received: September 2006;      Revised: April 2007;      Published: September 2007.