Uniqueness of Positive Solutions of Δu+f(u)=0 in ?N, N≦3 |
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Authors: | Carmen Cortázar Manuel Elgueta Patricio Felmer |
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Institution: | (1) Facultad de Matemáticas, Universidad Católica, Casilla 306 Correo 22, Santiago, Chile, CL;(2) Departamento de Ing. Matemática, F.C.F.M., Universidad de Chile, Casilla 170 Correo 3, Santiago, Chile, CL |
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Abstract: | We study the uniqueness of radial ground states for the semilinear elliptic partial differential equation in ℝ
N
. We assume that the function f has two zeros, the origin and u
0>0. Above u
0 the function f is positive, is locally Lipschitz continuous and satisfies convexity and growth conditions of a superlinear nature. Below
u
0, f is assumed to be non-positive, non-identically zero and merely continuous. Our results are obtained through a careful analysis
of the solutions of an associated initial‐value problem, and the use of a monotone separation theorem. It is known that, for
a large class of functions f, the ground states of (*) are radially symmetric. In these cases our result implies that (*) possesses at most one ground
state.
(Accepted July 3, 1996) |
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Keywords: | |
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