Geodesic
Nonexistence of solutions to KPP-type equations of dimension greater than or equal to one
Electronic journal of differential equations, Tome 2006 (2006)
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__a181,
     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},
     year = {2006},
     volume = {2006},
     zbl = {1284.35186},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2006__2006__a181/}
}
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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__a181/