| Title:
|
On periodic solutions of non-autonomous second order Hamiltonian systems (English) |
| Author:
|
Zhang, Xingyong |
| Author:
|
Zhou, Yinggao |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
55 |
| Issue:
|
5 |
| Year:
|
2010 |
| Pages:
|
373-384 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The purpose of this paper is to study the existence of periodic solutions for the non-autonomous second order Hamiltonian system \begin {equation*} \begin {cases} \ddot u(t)=\nabla F(t,u(t)),\enspace \text {a.e.} \ t\in [0,T],\\ u(0)-u(T)=\dot u(0)-\dot u(T)=0. \end {cases} \end {equation*} Some new existence theorems are obtained by the least action principle. (English) |
| Keyword:
|
periodic solution |
| Keyword:
|
critical point |
| Keyword:
|
non-autonomous second-order system |
| Keyword:
|
Sobolev inequality |
| MSC:
|
34C25 |
| MSC:
|
37J45 |
| MSC:
|
47J30 |
| MSC:
|
58E50 |
| idZBL:
|
Zbl 1224.34126 |
| idMR:
|
MR2737718 |
| DOI:
|
10.1007/s10492-010-0013-9 |
| . |
| Date available:
|
2010-11-24T08:13:23Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140708 |
| . |
| Reference:
|
[1] Berger, M. S., Schechter, M.: On the solvability of semilinear gradient operator equations.Adv. Math. 25 (1977), 97-132. Zbl 0354.47025, MR 0500336, 10.1016/0001-8708(77)90001-9 |
| Reference:
|
[2] Fonda, A., Gossez, J.-P.: Semicoercive variational problems at resonance: An abstract approach.Differ. Integral Equ. 3 (1990), 695-708. Zbl 0727.35056, MR 1044214 |
| Reference:
|
[3] Ma, J., Tang, C. L.: Periodic solution for some nonautonomous second-order systems.J. Math. Anal. Appl. 275 (2002), 482-494. MR 1943760, 10.1016/S0022-247X(02)00636-4 |
| Reference:
|
[4] Mawhin, J., Willem, M.: Critical Point Theory and Hamiltonian Systems.Springer Berlin (1989). Zbl 0676.58017, MR 0982267 |
| Reference:
|
[5] Rabinowitz, P. H.: On subharmonic solutions of Hamiltonian systems.Commun. Pure Appl. Math. 33 (1980), 609-633. Zbl 0425.34024, MR 0586414, 10.1002/cpa.3160330504 |
| Reference:
|
[6] Tang, C. L.: Periodic solution of non-autonomous second order systems with $\gamma$-quasisub-additive potential.J. Math. Anal. Appl. 189 (1995), 671-675. MR 1312546, 10.1006/jmaa.1995.1044 |
| Reference:
|
[7] Tang, C. L.: Periodic solution of non-autonomous second order system.J. Math. Anal. Appl. 202 (1996), 465-469. MR 1406241, 10.1006/jmaa.1996.0327 |
| Reference:
|
[8] Tang, C. L.: Existence and multiplicity of periodic solutions for nonautonomous second order systems.Nonlinear Anal., Theory Methods Appl. 32 (1998), 299-304. Zbl 0949.34032, MR 1610641, 10.1016/S0362-546X(97)00493-8 |
| Reference:
|
[9] Wu, X. P., Tang, C. L.: Periodic solution of a class of non-autonomous second order systems.J. Math. Anal. Appl. 236 (1999), 227-235. MR 1704579, 10.1006/jmaa.1999.6408 |
| Reference:
|
[10] Zhao, F. K., Wu, X.: Periodic solution for class of non-autonomous second order systems.J. Math. Anal. Appl. 296 (2004), 422-434. MR 2075174, 10.1016/j.jmaa.2004.01.041 |
| . |
