Nonexistence of solutions in $(0,1)$ for K-P-P-type equations for all $d\ge 1$

Details Nonexistence of solutions in $(0,1)$ for K-P-P-type equations for all $d\ge 1$ Nonexistence of solutions in $(0,1)$ for K-P-P-type equations for all $d\ge 1$

2005-09-16

arxiv.org/abs/math/0509384v1

Mathematics

Analysis of PDEs

6 pages

Scientific paper

Consider the KPP-type equation of the form $\Delta u+f(u)=0$, where $f:[0,1]
\to \mathbb R_{+}$ is a concave function. We prove for arbitrary dimensions
that there is no solution bounded in $(0,1)$. The significance of this result
from the point of view of probability theory is also discussed.

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