Existence of Homoclinic Orbits for a Class of Asymptotically ð ‘ -Linear Difference Systems with ð ‘ -Laplacian

Qiongfen Zhang and X. H. Tang

Abstract and Applied Analysis, 2011, vol. 2011, 1-17

Abstract:

By applying a variant version of Mountain Pass Theorem in critical point theory, we prove the existence of homoclinic solutions for the following asymptotically ð ‘ -linear difference system with ð ‘ -Laplacian Δ ( | Δ ð ‘¢ ( ð ‘› − 1 ) | ð ‘ âˆ’ 2 Δ ð ‘¢ ( ð ‘› − 1 ) ) + ∇ [ − ð ¾ ( ð ‘› , ð ‘¢ ( ð ‘› ) ) + ð ‘Š ( ð ‘› , ð ‘¢ ( ð ‘› ) ) ] = 0 , where ð ‘ âˆˆ ( 1 , + ∞ ) , ð ‘› ∈ ℤ , ð ‘¢ ∈ â„ ð ‘ , ð ¾ , ð ‘Š ∶ ℤ × â„ ð ‘ â†’ â„ are not periodic in ð ‘› , and W is asymptotically ð ‘ -linear at infinity.

Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:351562

DOI: 10.1155/2011/351562

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