Electron. J. Differential Equations, Vol. 2016 (2016), No. 315, pp. 1-10.

Existence of homoclinic orbits for a class of nonlinear functional difference equations

Xia Liu, Tao Zhou, Haiping Shi

By using critical point theory, we prove the existence of a nontrivial homoclinic orbit for a class of nonlinear functional difference equations. Our conditions on the nonlinear term do not need to satisfy the well-known global Ambrosetti-Rabinowitz superquadratic condition.

Submitted October 3, 2016. Published December 10, 2016.
Math Subject Classifications: 34C37, 37J45, 39A12, 47J30, 58E05.
Key Words: Homoclinic orbit; difference equation; critical point theory.

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Xia Liu
Oriental Science and Technology College
Hunan Agricultural University
Changsha 410128, China
email: xia991002@163.com
Tao Zhou
School of Business Administration
South China University of Technology
Guangzhou 510640, China
email: zhoutaoscut@hotmail.com
Haiping Shi
Modern Business and Management Department
Guangdong Construction Polytechnic
Guangzhou 510440, China
email: shp7971@163.com

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