Abstract and Applied Analysis

Ground State Solutions for the Periodic Discrete Nonlinear Schrödinger Equations with Superlinear Nonlinearities

Ali Mai and Zhan Zhou

Full-text: Open access

Abstract

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.

Article information

Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2013), Article ID 317139, 11 pages.

Dates
First available in Project Euclid: 26 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393449444

Digital Object Identifier
doi:10.1155/2013/317139

Mathematical Reviews number (MathSciNet)
MR3045046

Zentralblatt MATH identifier
1291.35356

Citation

Mai, Ali; Zhou, Zhan. Ground State Solutions for the Periodic Discrete Nonlinear Schrödinger Equations with Superlinear Nonlinearities. Abstr. Appl. Anal. 2013, Special Issue (2013), Article ID 317139, 11 pages. doi:10.1155/2013/317139. https://projecteuclid.org/euclid.aaa/1393449444


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