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

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  • 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 $(u_0,\infty)$.

    Mathematics Subject Classification: 37C45.


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