Zhang Liang and Chen Guanwei: Infinitely many homoclinic solutions for perturbed second-order Hamiltonian systems with subquadratic potentials. (2020)
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Abstract
In this paper, we consider the following perturbed second-order Hamiltonian system −u¨(t) + L(t)u = ∇W(t, u(t)) + ∇G(t, u(t)), ∀ t ∈ R, where W(t, u) is subquadratic near origin with respect to u; the perturbation term G(t, u) is only locally defined near the origin and may not be even in u. By using the variant Rabinowitz’s perturbation method, we establish a new criterion for guaranteeing that this perturbed second-order Hamiltonian system has infinitely many homoclinic solutions under broken symmetry situations. Our result improves some related results in the literature.
| Item Type: | Journal |
|---|---|
| Publication full: | Electronic journal of qualitative theory of differential equations |
| Date: | 2020 |
| Number: | 9 |
| ISSN: | 1417-3875 |
| DOI: | 10.14232/ejqtde.2020.1.9 |
| Uncontrolled Keywords: | Differenciaegyenlet, Rabinowitz perturbációs módszer, Hamilton-rendszer |
| Additional Information: | Bibliogr.: p. 21-23. ; összefoglalás angol nyelven |
| Date Deposited: | 2020. Jun. 08. 09:07 |
| Last Modified: | 2021. Oct. 20. 13:52 |
| URI: | http://acta.bibl.u-szeged.hu/id/eprint/69513 |
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