Homoclinic solutions for subquadratic Hamiltonian systems with competition potentials
In this paper, we consider of the following second-order Hamiltonian system u¨(t) − L(t)u(t) + ∇W(t, u(t)) = 0, ∀t ∈ R, where W(t, x) is subquadratic at infinity. With a competition condition, we establish the existence of homoclinic solutions by using the variational methods. In our theorem, the sm...
Elmentve itt :
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| Dokumentumtípus: | Folyóirat |
| Megjelent: |
2024
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| Sorozat: | Electronic journal of qualitative theory of differential equations
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| Kulcsszavak: | Hamilton-rendszer, Dinamikai rendszer, Differenciálegyenlet - ordinárius |
| Tárgyszavak: | |
| doi: | 10.14232/ejqtde.2024.1.5 |
| Online Access: | http://acta.bibl.u-szeged.hu/88807 |
| Tartalmi kivonat: | In this paper, we consider of the following second-order Hamiltonian system u¨(t) − L(t)u(t) + ∇W(t, u(t)) = 0, ∀t ∈ R, where W(t, x) is subquadratic at infinity. With a competition condition, we establish the existence of homoclinic solutions by using the variational methods. In our theorem, the smallest eigenvalue function l(t) of L(t) is not necessarily coercive or bounded from above and W(t, x) is not necessarily integrable on R with respect to t. Our theorem generalizes many known results in the references. |
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| Terjedelem/Fizikai jellemzők: | 13 |
| ISSN: | 1417-3875 |