Homoclinic solutions for second‐order discrete Hamiltonian systems with asymptotically quadratic potentials |
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Authors: | Huiwen Chen Zhimin He |
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Institution: | School of Mathematics and Statistics, Central South University, , Changsha, Hunan 410083, China |
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Abstract: | In this paper, we study the existence of infinitely many homoclinic solutions for the second‐order self‐adjoint discrete Hamiltonian system , where , and are unnecessarily positive definites for all . By using the variant fountain theorem, we obtain an existence criterion to guarantee that the aforementioned system has infinitely many homoclinic solutions under the assumption that W(n,x) is asymptotically quadratic as | x | → + ∞ . Copyright © 2013 John Wiley & Sons, Ltd. |
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Keywords: | homoclinic solutions discrete Hamiltonian systems variational methods asymptotically quadratic |
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