Electron. J. Diff. Eqns., Vol. 2006(2006), No. 09, pp. 1-6.

Nonexistence of solutions to KPP-type equations of dimension greater than or equal to one

Janos Englander, Peter L. Simon

In this article, we consider a semilinear elliptic equations of the form $\Delta u+f(u)=0$, where $f$ is a concave function. We prove for arbitrary dimensions that there is no solution bounded in $(0,1)$. The significance of this result in probability theory is also discussed.

Submitted September 19, 2005. Published January 24, 2006.
Math Subject Classifications: 35J60, 35J65, 60J80.
Key Words: KPP-equation; semilinear elliptic equations; positive bounded solutions; branching Brownian-motion.

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János Engländer
Department of Statistics and Applied Probability
University of California
Santa Barbara, CA 93106-3110, USA
email: englander@pstat.ucsb.edu
Péter L. Simon
Department of Applied Analysis, Eötvös Loránd University
Pázmány Péter Sétány 1/C, H-1117 Budapest, Hungary
email: simonp@cs.elte.hu

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