Homoclinic Orbits for a Class of Nonperiodic Hamiltonian Systems
We study the following nonperiodic Hamiltonian system ż=JHz(t,z), where H∈C1(R×R2N,R) is the form H(t,z)=(1/2)B(t)z⋅z+R(t,z). We introduce a new assumption on B(t) and prove that the corresponding Hamiltonian operator has only point spectrum. Moreover, by applying a generalized linking theorem for...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/769232 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832556987059011584 |
|---|---|
| author | Wenping Qin Jian Zhang Fukun Zhao |
| author_facet | Wenping Qin Jian Zhang Fukun Zhao |
| author_sort | Wenping Qin |
| collection | DOAJ |
| description | We study the following nonperiodic Hamiltonian system ż=JHz(t,z), where H∈C1(R×R2N,R) is the form H(t,z)=(1/2)B(t)z⋅z+R(t,z). We introduce a new assumption on B(t) and prove that the corresponding Hamiltonian operator has only point spectrum. Moreover, by applying a generalized linking theorem for strongly indefinite functionals, we establish the existence of homoclinic orbits for asymptotically quadratic nonlinearity as well as the existence of infinitely many homoclinic orbits for superquadratic nonlinearity. |
| format | Article |
| id | doaj-art-ddad02046af14bf194a96301c7d378ee |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-ddad02046af14bf194a96301c7d378ee2025-02-03T05:43:55ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/769232769232Homoclinic Orbits for a Class of Nonperiodic Hamiltonian SystemsWenping Qin0Jian Zhang1Fukun Zhao2Department of Mathematics, Yunnan Normal University, Yunnan, Kunming 650092, ChinaDepartment of Mathematics, Yunnan Normal University, Yunnan, Kunming 650092, ChinaDepartment of Mathematics, Yunnan Normal University, Yunnan, Kunming 650092, ChinaWe study the following nonperiodic Hamiltonian system ż=JHz(t,z), where H∈C1(R×R2N,R) is the form H(t,z)=(1/2)B(t)z⋅z+R(t,z). We introduce a new assumption on B(t) and prove that the corresponding Hamiltonian operator has only point spectrum. Moreover, by applying a generalized linking theorem for strongly indefinite functionals, we establish the existence of homoclinic orbits for asymptotically quadratic nonlinearity as well as the existence of infinitely many homoclinic orbits for superquadratic nonlinearity.http://dx.doi.org/10.1155/2012/769232 |
| spellingShingle | Wenping Qin Jian Zhang Fukun Zhao Homoclinic Orbits for a Class of Nonperiodic Hamiltonian Systems Abstract and Applied Analysis |
| title | Homoclinic Orbits for a Class of Nonperiodic Hamiltonian Systems |
| title_full | Homoclinic Orbits for a Class of Nonperiodic Hamiltonian Systems |
| title_fullStr | Homoclinic Orbits for a Class of Nonperiodic Hamiltonian Systems |
| title_full_unstemmed | Homoclinic Orbits for a Class of Nonperiodic Hamiltonian Systems |
| title_short | Homoclinic Orbits for a Class of Nonperiodic Hamiltonian Systems |
| title_sort | homoclinic orbits for a class of nonperiodic hamiltonian systems |
| url | http://dx.doi.org/10.1155/2012/769232 |
| work_keys_str_mv | AT wenpingqin homoclinicorbitsforaclassofnonperiodichamiltoniansystems AT jianzhang homoclinicorbitsforaclassofnonperiodichamiltoniansystems AT fukunzhao homoclinicorbitsforaclassofnonperiodichamiltoniansystems |