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Zbl 1248.35193
Byeon, Jaeyoung; Huh, Hyungjin; Seok, Jinmyoung
Standing waves of nonlinear Schrödinger equations with the gauge field. (English)
[J] J. Funct. Anal. 263, No. 6, 1575-1608 (2012). ISSN 0022-1236

Summary: We study standing waves for nonlinear Schrödinger equations with the gauge field. Some existence results of standing waves are established by applying variational methods to the functional which is obtained by representing the gauge field $A_{\mu }$ in terms of complex scalar field $\phi $. We also show that there exists no standing wave for certain range of parameters by establishing a new inequality of Sobolev type.

MSC 2000:: *35Q55 NLS-like (nonlinear Schroedinger) equations
35A15 Variational methods (PDE)
35A01

Keywords: Schrödinger; nonlocal potential; standing waves; variational methods

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