On the uniqueness of ground state solutions of a semilinear equation containing a  weighted Laplacian

C. Cortázar; Marta García-Huidobro

doi:10.3934/cpaa.2006.5.813

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2006, Volume 5, Issue 4: 813-826. Doi: 10.3934/cpaa.2006.5.813

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On the uniqueness of ground state solutions of a semilinear equation containing a weighted Laplacian

C. Cortázar^1, and
Marta García-Huidobro²

1.
Facultad de Matemáticas, Universidad Católica de Chile, Casilla 306, Correo 22 - Santiago
2.
Department of Mathematics, Pontificia Universidad Católica de Chile, Casilla 306, Correo 22, Santiago

Received: December 2004

Revised: May 2006

Published: December 2006

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Abstract

We consider the problem of uniqueness of radial ground state solutions to

(P) $ \qquad\qquad\qquad -\Delta u=K(|x|)f(u),\quad x\in \mathbb R^n.$

Here $K$ is a positive $C^1$ function defined in $\mathbb R^+$ and $f\in C[0,\infty)$ has one zero at $u_0>0$, is non positive and not identically 0 in $(0,u_0)$, and it is locally lipschitz, positive and satisfies some superlinear growth assumption in $(u_0,\infty)$.

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Mathematics Subject Classification: 37C45.

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