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Homoclinic Solutions for a Class of Nonlinear Difference Equations

Author

Listed:
  • Ali Mai
  • Zhan Zhou

Abstract

We prove the existence of homoclinic solutions of a class of nonlinear difference equations with superlinear nonlinearity by using the generalized Nehari manifold approach. For the case where the nonlinearity is odd, we obtain infinitely many homoclinic solutions of the equations. Recent results in the literature are generalized and improved.

Suggested Citation

  • Ali Mai & Zhan Zhou, 2014. "Homoclinic Solutions for a Class of Nonlinear Difference Equations," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnljam:v:2014:y:2014:i:1:n:749678
    DOI: 10.1155/2014/749678
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    References listed on IDEAS

    as
    1. Defang Ma & Zhan Zhou, 2012. "Existence and Multiplicity Results of Homoclinic Solutions for the DNLS Equations with Unbounded Potentials," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-15, October.
    2. Defang Ma & Zhan Zhou, 2012. "Existence and Multiplicity Results of Homoclinic Solutions for the DNLS Equations with Unbounded Potentials," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    3. Ali Mai & Zhan Zhou, 2013. "Ground State Solutions for the Periodic Discrete Nonlinear Schrödinger Equations with Superlinear Nonlinearities," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-11, April.
    4. 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).
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