On the uniqueness of ground state solutions of a semilinear equation containing a weighted Laplacian
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Date
2006
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Abstract
We consider the problem of uniqueness of radial ground state solutions to
(P) -Delta u = K(vertical bar x vertical bar)f(u), x is an element of R-n.
Here K is a positive C-1 function defined in R+ and f is an element of C[0, infinity) 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), infinity).
(P) -Delta u = K(vertical bar x vertical bar)f(u), x is an element of R-n.
Here K is a positive C-1 function defined in R+ and f is an element of C[0, infinity) 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), infinity).
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Keywords
ground state, uniqueness, superlinear, separation