Existence and multiplicity of homoclinic solutions for a second-order Hamiltonian system
In this paper, we find new conditions to ensure the existence of one nontrivial homoclinic solution and also infinitely many homoclinic solutions for the second order Hamiltonian system u¨ − a(t)|u| p−2u + ∇W(t, u) = 0, t ∈ R, where p > 2, a ∈ C(R, R) with inft∈R a(t) > 0 and R R 1 a(t) �2/(p−...
Elmentve itt :
| Szerző: | |
|---|---|
| Dokumentumtípus: | Folyóirat |
| Megjelent: |
2019
|
| Sorozat: | Electronic journal of qualitative theory of differential equations
|
| Kulcsszavak: | Hamilton-rendszer |
| doi: | 10.14232/ejqtde.2019.1.11 |
| Online Access: | http://acta.bibl.u-szeged.hu/58106 |
| Tartalmi kivonat: | In this paper, we find new conditions to ensure the existence of one nontrivial homoclinic solution and also infinitely many homoclinic solutions for the second order Hamiltonian system u¨ − a(t)|u| p−2u + ∇W(t, u) = 0, t ∈ R, where p > 2, a ∈ C(R, R) with inft∈R a(t) > 0 and R R 1 a(t) �2/(p−2) dt < +∞, and W(t, x) is, as |x| → ∞, superquadratic or subquadratic with certain hypotheses different from those used in previous related studies. Our approach is variational and we use the Cerami condition instead of the Palais–Smale one for deformation arguments. |
|---|---|
| Terjedelem/Fizikai jellemzők: | 1-26 |
| ISSN: | 1417-3875 |