On the uniqueness of the second bound state solution of a semilinear equation
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Date
2009
Journal Title
Journal ISSN
Volume Title
Publisher
ELSEVIER SCIENCE BV
Abstract
We establish the uniqueness of the second radial bound state solution of
Delta u + f (u) = 0, x is an element of R-n.
We assume that the nonlinearity f is an element of C(-infinity, infinity) is an odd function satisfying some convexity and growth conditions of superlinear type, and either has one zero at b > 0, is nonpositive and not identically 0 in (0, b), and is differentiable and positive [b, infinity), or is positive and differentiable in [0, infinity). (C) 2009 Elsevier Masson SAS. All rights reserved.
Delta u + f (u) = 0, x is an element of R-n.
We assume that the nonlinearity f is an element of C(-infinity, infinity) is an odd function satisfying some convexity and growth conditions of superlinear type, and either has one zero at b > 0, is nonpositive and not identically 0 in (0, b), and is differentiable and positive [b, infinity), or is positive and differentiable in [0, infinity). (C) 2009 Elsevier Masson SAS. All rights reserved.
Description
Keywords
Bound state, Uniqueness, Separation lemmas, LINEAR ELLIPTIC-EQUATIONS, POSITIVE RADIAL SOLUTIONS, GROUND-STATE, NONNEGATIVE SOLUTIONS, DELTA-U+F(U)=0, RN, EXISTENCE, LAPLACIAN, R(N)