Displaying similar documents to “On homoclinic solutions of a semilinear p -Laplacian difference equation with periodic coefficients.”

Homoclinic solutions of 2nth-order difference equations containing both advance and retardation

Yuhua Long, Yuanbiao Zhang, Haiping Shi (2016)

Open Mathematics

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By using the critical point method, some new criteria are obtained for the existence and multiplicity of homoclinic solutions to a 2nth-order nonlinear difference equation. The proof is based on the Mountain Pass Lemma in combination with periodic approximations. Our results extend and improve some known ones.