Homoclinic solutions of 2<i>n</i>th-order difference equations containing both advance and retardation

Ye, Long; Yuan-biao, Zhang; Shi, Haiping

doi:10.1515/math-2016-0046

Cited by 5 publications

(2 citation statements)

References 31 publications

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“…We also point out that the condition (f 1 ) in Theorem 6.1 was first introduced by Guo and Xu in [49], where they discussed the existence of periodic solutions to a class of second order neutral differential difference equations. Since then, many variants of the condition (f 1 ) have been frequently used in the study of nonlinear difference equations containing both advances and delays, see for example [28,62,71,85,95,107,117].…”

Section: Theorem 53 ([123]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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Section: Theorem 53 ([123]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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“…Recently, some literature [11,12] studied solutions of φ c -Laplacian difference equations. For more research on solutions of difference equations, we can refer to [13][14][15][16][17][18][19][20][21][28][29][30][31].…”

Section: Introductionmentioning

confidence: 99%

Multiple solutions of fourth-order difference equations with different boundary conditions

Wang

Chen

2019

Bound Value Probl

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In the present paper, a class of fourth-order nonlinear difference equations with Dirichlet boundary conditions or periodic boundary conditions are considered. Based on the invariant sets of descending flow in combination with the mountain pass lemma, we establish a series of sufficient conditions on the existence of multiple solutions for these boundary value problems. In addition, some examples are provided to demonstrate the applicability of our results.

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Multiple solutions of fourth-order functional difference equation with periodic boundary conditions

Wang

2020

Applied Mathematics Letters

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Homoclinic solutions of 2nth-order difference equations containing both advance and retardation

Cited by 5 publications

References 31 publications

On variational and topological methods in nonlinear difference equations

On variational and topological methods in nonlinear difference equations

Multiple solutions of fourth-order difference equations with different boundary conditions

Multiple solutions of fourth-order functional difference equation with periodic boundary conditions

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