Standing Waves for Nonlinear Schrodinger Equations with a General Nonlinearity: One and Two Dimensional Cases

Authors :: Louis Jeanjean
Jaeyoung Byeon
Kazunaga Tanaka
Department of Mathematics, Pohang University of Science and Technology, Pohang
Laboratoire de Mathématiques de Besançon (UMR 6623) (LMB)
Université de Bourgogne (UB)-Université de Franche-Comté (UFC)
Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université Bourgogne Franche-Comté [COMUE] (UBFC)-Centre National de la Recherche Scientifique (CNRS)
Department of Mathematics, School of Science and Engineering, Waseda University
Source :: Communications in Partial Differential Equations, Communications in Partial Differential Equations, Taylor & Francis, 2008, 33 (6), pp.1113-1136. ⟨10.1080/03605300701518174⟩
Publication Year :: 2008
Publisher :: Informa UK Limited, 2008.
Abstract: For N = 1,2, we consider singularly perturbed elliptic equations ϵ2Δ u − V(x) u + f(u)= 0, u(x)> 0 on R N , lim|x|→∞ u(x)= 0. For small ϵ > 0, we show the existence of a localized bound state solut...

Subjects :: Applied Mathematics
010102 general mathematics
Mathematical analysis
01 natural sciences
Schrödinger equation
010101 applied mathematics
Standing wave
Nonlinear system
symbols.namesake
Bound state
symbols
[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]
0101 mathematics
ComputingMilieux_MISCELLANEOUS
Analysis
Mathematics

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