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Homoclinic orbits and subharmonics for nonlinear second order difference equations |
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| Authors: | Manjun ma Zhiming Guo |
| Affiliation: | 1. Department of Physics–Mathematics, Nanhua University, Hengyang, Hunan 421001, People’s Republic of China;2. School of Mathematics and Information Science, Guangzhou University, Guangzhou 510405, People’s Republic of China |
| Abstract: | We show the existence of a nontrivial homoclinic orbit and subharmonic solutions for a class of second order difference equations by applying the “Mountain Pass” theorem relying on Ekeland’s variational principle and the diagonal method, and the homoclinic orbit as the limit of the subharmonics. A completely new way is provided for dealing with the existence of solutions for difference equations. |
| Keywords: | Discrete variational method Diagonal method Homoclinic orbits Subharmonics Nonlinear difference equations |
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