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

J. Englander; P. L. Simon

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

Analysis of PDEs 2007-05-23 v1 Probability

Authors: J. Englander , P. L. Simon

Abstract

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.

Keywords

kpp-type equation nonexistence of solutions concave nonlinearity elliptic pde bounded solution

Cite

@article{arxiv.math/0509384,
  title  = {Nonexistence of solutions in $(0,1)$ for K-P-P-type equations for all $d\ge 1$},
  author = {J. Englander and P. L. Simon},
  journal= {arXiv preprint arXiv:math/0509384},
  year   = {2007}
}

Comments

6 pages

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