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Infinitely Many Homoclinic Orbits for 2 th-Order Nonlinear Functional Difference Equations Involving the -Laplacian

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  • Xiaofei He

Abstract

By establishing a new proper variational framework and using the critical point theory, we establish some new existence criteria to guarantee that the 2 th-order nonlinear difference equation containing both advance and retardation with -Laplacian , , , has infinitely many homoclinic orbits, where is -Laplacian operator; , , are nonperiodic in . Our conditions on the potential are rather relaxed, and some existing results in the literature are improved.

Suggested Citation

  • Xiaofei He, 2012. "Infinitely Many Homoclinic Orbits for 2 th-Order Nonlinear Functional Difference Equations Involving the -Laplacian," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-20, January.
    • Handle: RePEc:hin:jnlaaa:297618
    DOI: 10.1155/2012/297618
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