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- Title
Semi-classical standing waves for nonlinear Schrödinger equations at structurally stable critical points of the potential.
- Authors
Jaeyoung Byeon; Kazunaga Tanaka
- Abstract
We consider a singularly perturbed elliptic equation Berestycki-Lions [3] found almost necessary and sufficient conditions on the nonlinearity f for existence of a solution of the limiting problem. There have been endeavors to construct solutions of the singularly perturbed problem concentrating around structurally stable critical points of the potential V under possibly general conditions on f. In this paper, we prove that under the optimal conditions of Berestycki-Lions on f 2 C1, there exists a solution concentrating around topologically stable positive critical points of V, whose critical values are characterized by minimax methods.
- Subjects
SCHRODINGER equation; CRITICAL point theory; PERTURBATION theory; TOPOLOGY; STABILITY theory
- Publication
Journal of the European Mathematical Society (EMS Publishing), 2013, Vol 15, Issue 5, p1859
- ISSN
1435-9855
- Publication type
Article
- DOI
10.4171/JEMS/407