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.


39A12 Discrete version of topics in analysis
39A11 Stability of difference equations (MSC2000)
37J05 Relations of dynamical systems with symplectic geometry and topology (MSC2010)
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