Communications on Pure and Applied Analysis (CPAA)

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

Pages: 813 - 826, Volume 5, Issue 4, December 2006      doi:10.3934/cpaa.2006.5.813

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C. Cortázar - Facultad de Matemáticas, Universidad Católica de Chile, Casilla 306, Correo 22 - Santiago, Chile (email)
Marta García-Huidobro - Department of Mathematics, Pontificia Universidad Católica de Chile, Casilla 306, Correo 22, Santiago, Chile (email)

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 $(u_0,\infty)$.

Keywords:  Ground state, uniqueness, superlinear, separation.
Mathematics Subject Classification:  37C45.

Received: December 2004;      Revised: May 2006;      Available Online: September 2006.