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Homoclinic orbits for nonlinear difference equations containing both advance and retardation |
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| Authors: | Jianshe Yu Haiping Shi Zhiming Guo |
| Institution: | a Basic Courses Department, Guangdong Baiyun Institute, Guangzhou 510450, PR China b College of Mathematics and Econometrics, Hunan University, Changsha 410082, PR China c School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, PR China |
| Abstract: | In this paper we discuss how to use the critical point theory to study the existence of a nontrivial homoclinic orbit for nonlinear difference equations containing both advance and retardation without any periodic assumptions. Moreover, if the nonlinearity is an odd function, the existence of an unbounded sequence of homoclinic orbits is obtained. |
| Keywords: | Homoclinic orbits Nonlinear difference equations Advance and retardation Variational structure Critical point |
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