Standing waves for nonlinear Schrodinger equations with a general nonlinearity: One and two dimensional cases
SCIE
SCOPUS
- Title
- Standing waves for nonlinear Schrodinger equations with a general nonlinearity: One and two dimensional cases
- Authors
- Byeon, J; Jeanjean, L; Tanaka, K
- Date Issued
- 2008-01
- Publisher
- TAYLOR & FRANCIS INC
- Abstract
- For N=1,2, we consider singularly perturbed elliptic equations epsilon(2) Delta u-V(x) u+f(u)=0, u(x)> 0 on R-N, lim(vertical bar x vertical bar ->infinity) u(x)=0. For small epsilon > 0, we show the existence of a localized bound state solution concentrating at an isolated component of positive local minimum of V under conditions on f we believe to be almost optimal; when N >= 3, it was shown in Byeon and Jeanjean (2007).
- Keywords
- Berestycki-Lions conditions; nonlinear Schrodinger equations; standing waves; variational methods; SEMICLASSICAL STATES; CRITICAL FREQUENCY; BOUND-STATES; ELLIPTIC PROBLEMS; FIELD-EQUATIONS; R-N; EXISTENCE; R(N)
- URI
- https://oasis.postech.ac.kr/handle/2014.oak/29329
- DOI
- 10.1080/036053007015
- ISSN
- 0360-5302
- Article Type
- Article
- Citation
- COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, vol. 33, no. 6, page. 1113 - 1136, 2008-01
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