Electronic Journal of Differential Equations,
Vol. 2006(2006), No. 09, pp. 1-6.

Title: Nonexistence of solutions to KPP-type equations
       of dimension greater than or equal to one
       
Authors: Janos Englander (Univ. of California, Santa Barbara, CA, USA)
         Peter L. Simon (Eotvos Lorand Univ., Budapest, Hungary)

Abstract: 
 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.