March  2006, 5(1): 71-84. doi: 10.3934/cpaa.2006.5.71

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

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, Chile

Received  December 2004 Revised  August 2005 Published  December 2005

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

$(P)\qquad\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 $(u_0,\infty)$.

Citation: C. Cortázar, Marta García-Huidobro. On the uniqueness of ground state solutions of a semilinear equation containing a weighted Laplacian. Communications on Pure & Applied Analysis, 2006, 5 (1) : 71-84. doi: 10.3934/cpaa.2006.5.71
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