Ground state solutions for the periodic discrete nonlinear Schrödinger equations with superlinear nonlinearities. (English) Zbl 1291.35356

Mai, Ali; Zhou, Zhan

Abstr. Appl. Anal. 2013, Article ID 317139, 11 p. (2013).

Summary: We consider the periodic discrete nonlinear Schrödinger equations with the temporal frequency belonging to a spectral gap. By using the generalized Nehari manifold approach developed by Szulkin and Weth, we prove the existence of ground state solutions of the equations. We obtain infinitely many geometrically distinct solutions of the equations when specially the nonlinearity is odd. The classical Ambrosetti-Rabinowitz superlinear condition is improved.

MSC:

35Q55	NLS equations (nonlinear Schrödinger equations)
34L40	Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.)
34A33	Ordinary lattice differential equations
39A12	Discrete version of topics in analysis
39A70	Difference operators

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