Existence of Homoclinic Orbits for a Class of Asymptotically p‐Linear Difference Systems with p‐Laplacian

Qiongfen Zhang and X. H. Tang

Abstract and Applied Analysis, 2011, vol. 2011, issue 1

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 p‐linear difference system with p‐Laplacian Δ(|Δu(n − 1)|p−2Δu(n − 1))+∇[−K(n, u(n)) + W(n, u(n))] = 0, where p ∈ (1, +∞), n ∈ ℤ, u ∈ ℝN, K, W : ℤ × ℝN → ℝ are not periodic in n, and W is asymptotically p‐linear at infinity.

Date: 2011
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https://doi.org/10.1155/2011/351562

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2011:y:2011:i:1:n:351562

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