Standing waves with a critical frequency for nonlinear Schrodinger equations
SCIE
SCOPUS
- Title
- Standing waves with a critical frequency for nonlinear Schrodinger equations
- Authors
- Byeon, J; Wang, ZQ
- Date Issued
- 2002-12
- Publisher
- SPRINGER-VERLAG
- Abstract
- This paper is concerned with the existence and qualitative property of standing wave solutions psi(t, x) = e(-iEt/h)v(x) for the nonlinear Schrodinger equation (h) over bar +(h) over bar (2)/2 Deltapsi - V(x)psi + \psi\(p-1) psi = 0 with E being a critical frequency in the sense that min(RN) V(X) = E. We show that there exists a standing wave which is trapped in a neighbourhood of isolated minimum points of V and whose amplitude goes to 0 as (h) over bar --> 0. Moreover, depending upon the local behaviour of the potential function V (x) near the minimum points, the limiting profile of the standing-wave solutions will be shown to exhibit quite different characteristic features. This is in striking contrast with the non-critical frequency case (inf(RN) V (X) > E) which has been extensively studied in recent years.
- Keywords
- CONCENTRATION-COMPACTNESS PRINCIPLE; MULTI-BUMP SOLUTIONS; POSITIVE SOLUTIONS; BOUND-STATES; SEMICLASSICAL STATES; ELLIPTIC-EQUATIONS; EXISTENCE; CALCULUS; DOMAINS
- URI
- https://oasis.postech.ac.kr/handle/2014.oak/29802
- DOI
- 10.1007/S00205-002-0
- ISSN
- 0003-9527
- Article Type
- Article
- Citation
- ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, vol. 165, no. 4, page. 295 - 316, 2002-12
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