Infinitely many homoclinic solutions for perturbed second-order Hamiltonian systems with subquadratic potentials
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 usin...
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| Dokumentumtípus: | Folyóirat |
| Megjelent: |
2020
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| Sorozat: | Electronic journal of qualitative theory of differential equations
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| Kulcsszavak: | Differenciaegyenlet, Rabinowitz perturbációs módszer, Hamilton-rendszer |
| doi: | 10.14232/ejqtde.2020.1.9 |
| Online Access: | http://acta.bibl.u-szeged.hu/69513 |
| Tartalmi kivonat: | 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. |
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| ISSN: | 1417-3875 |