# American Institute of Mathematical Sciences

2007, 2007(Special): 974-981. doi: 10.3934/proc.2007.2007.974

## Positive solutions of elliptic equations with a critical oscillatory nonlinearity

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

Received  September 2006 Revised  April 2007 Published  September 2007

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}.
Citation: Kyril Tintarev. Positive solutions of elliptic equations with a critical oscillatory nonlinearity. Conference Publications, 2007, 2007 (Special) : 974-981. doi: 10.3934/proc.2007.2007.974
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