Periodic solutions for second-order difference equations with resonance at infinity

Tan, Fenghua; Guo, Zhiming

doi:10.1080/10236191003730498

Cited by 5 publications

(2 citation statements)

References 26 publications

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“…the existence and multiplicity of periodic solutions with prescribed minimal period has been studied by Yu, Long and Guo in [106]. By using a similar method, Tan and Guo obtained some multiplicity results in [87] when f was also resonant at infinity. Readers who are interested in these topics are referred to [68,70] and references therein.…”

Section: Theorem 35 ([48]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 35 ([48]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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“…It is well known that the resonance exists in many realworld applications, and the equations with resonance have been extensively studied in various fields [17][18][19][20][21]. In fact, it is more difficult to study the boundary value problem under the case of resonance because the resonance case can change the local geometric properties of the critical points [17].…”

Section: Introductionmentioning

confidence: 99%

Boundary Value Problem for a Second-Order Difference Equation with Resonance

Wang

Zhou

2020

Complexity

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Standing Waves Solutions for the Discrete Schrödinger Equations with Resonance

Wang¹,

2023

Bull. Malays. Math. Sci. Soc.

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In this paper, by using linking methods, we obtain the existence of the nontrivial standing wave solutions for the discrete nonlinear Schrödinger equations with resonance and unbounded potentials. In order to prove the existence of standing wave solutions, we give resonant condition to find a bounded critical sequence, and we show that such a sequence guarantees the existence of one nontrivial standing wave solution in $$l^{2}$$ l 2 when the nonlinearity is resonant and the potential is unbounded. To the best of the our knowledge, there is no existence results for the discrete nonlinear Schrödinger equations with resonance in the literature.

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Periodic solutions for second-order difference equations with resonance at infinity

Abstract: By using the critical point theory and a Z p geometrical index theory, some sufficient conditions are obtained for the existence and multiplicity of periodic solutions to the following non-linear second-order difference equationRÞ is resonant at infinity.

Cited by 5 publications

References 26 publications

On variational and topological methods in nonlinear difference equations

On variational and topological methods in nonlinear difference equations

Boundary Value Problem for a Second-Order Difference Equation with Resonance

Standing Waves Solutions for the Discrete Schrödinger Equations with Resonance

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