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

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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.
Classification : 35J60, 35J65, 60J80
Keywords: KPP-equation, semilinear elliptic equations, positive bounded solutions, branching Brownian-motion 
@article{EJDE_2006__2006__a81,
     author = {Engl\"ander, J\'anos and Simon, P\'eter L.},
     title = {Nonexistence of solutions to {KPP-type} equations of dimension greater than or equal to one},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2006},
     year = {2006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2006__2006__a81/}
}
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Engländer, János; Simon, Péter L. Nonexistence of solutions to KPP-type equations of dimension greater than or equal to one. Electronic Journal of Differential Equations, Tome 2006 (2006). http://geodesic.mathdoc.fr/item/EJDE_2006__2006__a81/