Existence of solutions to boundary value problems for a higher-dimensional difference system

Volume 10, Issue 10, pp 5576--5584 http://dx.doi.org/10.22436/jnsa.010.10.37

Publication Date: October 31, 2017 Submission Date: January 05, 2017

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Authors

Tao Zhou - School of Business Administration, South China University of Technology, Guangzhou 510640, China. Xia Liu - Oriental Science and Technology College, Hunan Agricultural University, Changsha 410128, China. - Science College, Hunan Agricultural University, Changsha 410128, 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

• Boundary value problems
• higher-dimensional
• mountain pass lemma
• critical point theory

MSC

•  39A10
•  47J30
•  58E05

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