Electronic Journal of Differential Equations (Jan 2006)
Nonexistence of solutions to KPP-type equations of dimension greater than or equal to one
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.
