Existence of homoclinic orbits for a higher order difference system

Volume 10, Issue 4, pp 1842--1853 http://dx.doi.org/10.22436/jnsa.010.04.44

Publication Date: April 20, 2017 Submission Date: January 19, 2017

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Authors

Xia Liu - Oriental Science and Technology College, Hunan Agricultural University, Changsha 410128, China. - Science College, Hunan Agricultural University, Changsha 410128, China. Tao Zhou - School of Business Administration, South China University of Technology, Guangzhou 510640, China. Haiping Shi - Modern Business and Management Department, Guangdong Construction Polytechnic, Guangzhou 510440, China.

Abstract

By using critical point theory, some new criteria are obtained for the existence of a nontrivial homoclinic orbit to a higher order difference system containing both many advances and retardations. The proof is based on the mountain pass lemma in combination with periodic approximations. Related results in the literature are generalized and improved.

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Keywords

• Homoclinic orbits
• higher order difference systems
• critical point theory
• advances and retardations.

MSC

•  34C37
•  37J45
•  39A12

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