Existence of periodic solutions for a class of second-order discrete Hamiltonian systems

Gu, Haiwei; An, Tianqing

doi:10.1080/10236198.2014.993322

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Theorem 31 ([122]1

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Cited by 6 publications

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“…In 2015, Gu and An ( [44]) made use of the Variant Fountain Theorem (cf. [13,14]) to study the existence of periodic solutions of (5) in the superquadratic case, where they assume that…”

Section: Theorem 31 ([122]mentioning

confidence: 99%

On variational and topological methods in nonlinear difference equations

Balanov¹,

García-Azpeitia²,

Krawcewicz³

2018

Communications on Pure &Amp; Applied Analysis

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In this paper, first we survey the recent progress in usage of the critical point theory to study the existence of multiple periodic and subharmonic solutions in second order difference equations and discrete Hamiltonian systems with variational structure. Next, we propose a new topological method, based on the application of the equivariant version of the Brouwer degree to study difference equations without an extra assumption on variational structure. New result on the existence of multiple periodic solutions in difference systems (without assuming that they are their variational) satisfying a Nagumo-type condition is obtained. Finally, we also put forward a new direction for further investigations.

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“…In 2015, Gu and An ( [44]) made use of the Variant Fountain Theorem (cf. [13,14]) to study the existence of periodic solutions of (5) in the superquadratic case, where they assume that…”

Section: Theorem 31 ([122]mentioning

confidence: 99%