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

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  • Ali Mai
  • Zhan Zhou

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.

Suggested Citation

  • Ali Mai & Zhan Zhou, 2013. "Ground State Solutions for the Periodic Discrete Nonlinear Schrödinger Equations with Superlinear Nonlinearities," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:317139
    DOI: 10.1155/2013/317139
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    References listed on IDEAS

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    1. Li He & Wanping Liu, 2011. "Periodic Solutions to a Third-Order Conditional Difference Equation over the Integers," Discrete Dynamics in Nature and Society, Hindawi, vol. 2011, pages 1-12, October.
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    Cited by:

    1. Guowei Sun, 2013. "On Standing Wave Solutions for Discrete Nonlinear Schrödinger Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    2. Genghong Lin & Zhan Zhou, 2014. "Homoclinic Solutions of a Class of Nonperiodic Discrete Nonlinear Systems in Infinite Higher Dimensional Lattices," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    3. Ali Mai & Zhan Zhou, 2014. "Homoclinic Solutions for a Class of Nonlinear Difference Equations," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).

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