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Existence of gap solitons in periodic discrete nonlinear Schrödinger equations. (English) Zbl 1178.35351

Summary: We discuss how to use critical point theory to study the existence of gap solitons for periodic discrete nonlinear Schrödinger equations. An open problem proposed by Professor Alexander Pankov is solved [A. Pankov, Nonlinearity 19, No. 1, 27–40 (2006; Zbl 1220.35163)].

MSC:

35Q55 NLS equations (nonlinear Schrödinger equations)
35A15 Variational methods applied to PDEs
58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
39A12 Discrete version of topics in analysis

Citations:

Zbl 1220.35163
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References:

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