Periodic Solutions with Minimal Period for Fourth-Order Nonlinear Difference Equations

Liu, Xia; Zhou, Tao; Shi, Haiping; Ye, Long; Wen, Zongliang

doi:10.1155/2018/4376156

Cited by 3 publications

(1 citation statement)

References 26 publications

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“…which is used to describe the stationary states of the deflection of an elastic beam [1]. As to difference equation (1.1), [2] establishes the existence of periodic solutions with mini-mal period by employing variational techniques and the linking theorem. Using Dancer's global bifurcation theorem, [3] shows the existence and multiplicity of positive solutions of (1.1) in the form of 4 x(n -2) = λh(n)f x(n) , n ∈ [2, N].…”

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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Section: Introductionmentioning

confidence: 99%

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

Wang

Chen

2019

Bound Value Probl

Self Cite

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Multiplicity and minimality of periodic solutions to fourth-order super-quadratic difference systems

Ling

Yuncheng

et al. 2022

Open Mathematics

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Three Solutions for a Partial Discrete Dirichlet Problem Involving the Mean Curvature Operator

Wang

Zhou

2021

Mathematics

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Partial difference equations have received more and more attention in recent years due to their extensive applications in diverse areas. In this paper, we consider a Dirichlet boundary value problem of the partial difference equation involving the mean curvature operator. By applying critical point theory, the existence of at least three solutions is obtained. Furthermore, under some appropriate assumptions on the nonlinearity, we respectively show that this problem admits at least two or three positive solutions by means of a strong maximum principle. Finally, we present two concrete examples and combine with images to illustrate our main results.

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Periodic Solutions with Minimal Period for Fourth-Order Nonlinear Difference Equations

Abstract: A fourth-order nonlinear difference equation is considered. By making use of critical point theory, some new criteria are obtained for the existence of periodic solutions with minimal period. The main methods used are a variational technique and the Linking Theorem.

Cited by 3 publications

References 26 publications

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

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

Multiplicity and minimality of periodic solutions to fourth-order super-quadratic difference systems

Three Solutions for a Partial Discrete Dirichlet Problem Involving the Mean Curvature Operator

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