On the uniqueness of sign changing bound state solutions of a semilinear equation
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Date
2011
Journal Title
Journal ISSN
Volume Title
Publisher
GAUTHIER-VILLARS/EDITIONS ELSEVIER
Abstract
We establish the uniqueness of the higher radial bound state solutions of
Delta u + f(u) = 0. x is an element of R".
We assume that the nonlinearity f is an element of C(-infinity. infinity) is an odd function satisfying some convexity and growth conditions, and has one zero at b > O. is nonpositive and not-identically 0 in (0. b). positive in [b. infinity). and is differentiable in (0. infinity). (C) 2011 Elsevier Masson SAS. All rights reserved.
Delta u + f(u) = 0. x is an element of R".
We assume that the nonlinearity f is an element of C(-infinity. infinity) is an odd function satisfying some convexity and growth conditions, and has one zero at b > O. is nonpositive and not-identically 0 in (0. b). positive in [b. infinity). and is differentiable in (0. infinity). (C) 2011 Elsevier Masson SAS. All rights reserved.
Description
Keywords
LINEAR ELLIPTIC-EQUATIONS, POSITIVE RADIAL SOLUTIONS, GROUND-STATE, NONNEGATIVE SOLUTIONS, DELTA-U+F(U)=0, RN, EXISTENCE, LAPLACIAN, R(N)