×

The existence of periodic and subharmonic solutions to subquadratic discrete Hamiltonian systems. (English) Zbl 1081.39019

The behaviour of a discrete system is sometimes sharply different to the behaviour of the corresponding continuous system. Many scholars have investigated discrete Hamiltonian systems for disconjugacy boundary value problems, oscillations and asymptotic behaviour. The critical point theory is an important tool for dealing with the existence of periodic solutions of differential equations. In this paper the authors use critical point theory to prove the existence of periodic and subharmonic solutions to subquadratic discrete Hamiltonian systems.

MSC:

39A12 Discrete version of topics in analysis
39A11 Stability of difference equations (MSC2000)
37J05 Relations of dynamical systems with symplectic geometry and topology (MSC2010)
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] DOI: 10.1007/BF01389883 · Zbl 0465.49006
[2] DOI: 10.1006/jmaa.1996.0177 · Zbl 0855.39018
[3] DOI: 10.1016/S0898-1221(01)00191-2 · Zbl 1005.39006
[4] Agarwal, Difference equations and inequalities: theory, methods and applications (2000) · Zbl 0952.39001
[5] Zhou, Dyn. Contin. Discrete Impuls. Syst. Ser. B 10 pp 95– (2005)
[6] DOI: 10.1080/10236190290017487 · Zbl 1005.39015
[7] DOI: 10.1002/cpa.3160330504 · Zbl 0425.34024
[8] DOI: 10.1002/cpa.3160310203
[9] Mawhin, Critical point theory and Hamiltonian systems (1989)
[10] DOI: 10.2307/1997963
[11] Guo, Science in China 46 pp 506– (2005) · Zbl 1215.39001
[12] DOI: 10.1016/j.na.2003.07.019 · Zbl 1053.39011
[13] DOI: 10.1016/0022-247X(92)90212-V · Zbl 0762.39003
[14] DOI: 10.1006/jdeq.1994.1018 · Zbl 0791.39001
[15] Chang, Critical point theory and its applications (1980)
[16] Ahlbrandt, Discrete Hamiltonian systems (1996) · Zbl 0860.39001
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.