Positive solutions of elliptic equations with a critical oscillatory nonlinearity

Pages: 974 - 981, Issue Special, September 2007

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Kyril Tintarev - Department of Mathematics, Uppsala University, P.O. Box 480, 751 06 Uppsala, Sweden (email)

Abstract: We prove existence of a counterpart of the Talenti solution in the critical semilinear problem −$\Delatu = f(u)$ in $\mathbb{R}^N$, $N$ > 3, where the nonlinearity $f$ oscillates about the critical "stem" $f(s) = s^((N+2)/(N − 2))$ : specifically, $f(2^((N − 2)/2j)s) = 2^(( N + 2)/ 2 j)f(s)$ for all $j \in \mathbb{Z}$, $s \in \mathb{R}.

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.