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A symmetry-breaking phenomenon and asymptotic profiles of least-energy solutions to a nonlinear Schrödinger equation

Published online by Cambridge University Press:  12 July 2007

Kazuhiro Kurata ,
Tatsuya Watanabe  and
Masataka Shibata
Kazuhiro Kurata
Affiliation:
Department of Mathematics, Tokyo Metropolitan University, 1-1 Minami-osawa, Hachioji-shi, Tokyo 192-0397, Japan
Tatsuya Watanabe
Affiliation:
Department of Mathematics, Tokyo Metropolitan University, 1-1 Minami-osawa, Hachioji-shi, Tokyo 192-0397, Japan
Masataka Shibata
Affiliation:
Department of Mathematics, Tokyo Institute of Technology University, 2-12-1 Oh-okayama, Meguro-ku, Tokyo 152-8551, Japan
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Abstract

In this paper, we study a symmetry-breaking phenomenon of a least-energy solution to a nonlinear Schrödinger equation under suitable assumptions on V(x), where λ > 1, p > 2 and χA is the characteristic function of the set A = [−(l + 2), −l] ∪ [l,l + 2] with l > 0. We also study asymptotic profiles of least-energy solutions for the singularly perturbed problem for small ε > 0.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 135 , Issue 2 , April 2005 , pp. 357 - 392
Copyright
Copyright © Royal Society of Edinburgh 2005

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