PERIODIC SOLUTIONS OF SECOND ORDER SELF-ADJOINT DIFFERENCE EQUATIONS

JIANSHE YU; ZHIMING GUO; XINGFU ZOU

doi:10.1112/S0024610704005939

Abstract

Using critical point theory, some sufficient conditions are obtained for the existence of nonconstant $T$-periodic solutions of a class of second order self-adjoint difference equations.

Footnotes

This project was partially supported by TRATOYT of China, by the Trans-Century Training Program Foundation of China, by the NSERC of Canada and by a Petro-Canada Young Innovator Award.

Crossref Citations

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Ma, Manjun and Guo, Zhiming 2006. Homoclinic orbits for second order self-adjoint difference equations. Journal of Mathematical Analysis and Applications, Vol. 323, Issue. 1, p. 513.

ma, Manjun and Guo, Zhiming 2007. Homoclinic orbits and subharmonics for nonlinear second order difference equations. Nonlinear Analysis: Theory, Methods & Applications, Vol. 67, Issue. 6, p. 1737.

Tian, Yu Du, Zengji and Ge, Weigao 2007. Existence results for discrete Sturm–Liouville problem via variational methods. Journal of Difference Equations and Applications, Vol. 13, Issue. 6, p. 467.

Ma, Manjun Tang, Hengsheng and Luo, Wei 2007. Periodic solutions for nonlinear second-order difference equations. Applied Mathematics and Computation, Vol. 184, Issue. 2, p. 685.

Xue, Yan-Fang and Tang, Chun-Lei 2007. Existence of a periodic solution for subquadratic second-order discrete Hamiltonian system. Nonlinear Analysis: Theory, Methods & Applications, Vol. 67, Issue. 7, p. 2072.

Deng, Xiaoqing and Cheng, Gong 2008. Homoclinic Orbits for Second Order Discrete Hamiltonian Systems with Potential Changing Sign. Acta Applicandae Mathematicae, Vol. 103, Issue. 3, p. 301.

Liu, Xi-Lan Wu, Jian-Hua and Zhang, Bing-Gen 2008. Uniqueness and Multiplicity of Solutions for a Second‐Order Discrete Boundary Value Problem with a Parameter. Discrete Dynamics in Nature and Society, Vol. 2008, Issue. 1,

Li, Xiong and Zhang, Jing 2009. Periodic solutions of some second order difference equations. Journal of Difference Equations and Applications, Vol. 15, Issue. 6, p. 579.

He, Tieshan Yang, Fengjian and Berezansky, Leonid 2009. Existence of Solutions to Boundary Value Problems for the Discrete Generalized Emden‐Fowler Equation. Discrete Dynamics in Nature and Society, Vol. 2009, Issue. 1,

Deng, Xiaoqing Cheng, Gong and Shi, Haiping 2009. Subharmonic solutions and homoclinic orbits of second order discrete Hamiltonian systems with potential changing sign. Computers & Mathematics with Applications, Vol. 58, Issue. 6, p. 1198.

He, Xiumei and Wu, Xian 2009. Existence and multiplicity of solutions for nonlinear second order difference boundary value problems. Computers & Mathematics with Applications, Vol. 57, Issue. 1, p. 1.

Yang, Minbo Zhao, Fukun and Ding, Yanheng 2010. Infinitely many stationary solutions of discrete vector nonlinear Schrödinger equation with symmetry. Applied Mathematics and Computation, Vol. 215, Issue. 12, p. 4230.

Tang, X.H. Lin, Xiaoyan and Xiao, Li 2010. Homoclinic solutions for a class of second order discrete Hamiltonian systems. Journal of Difference Equations and Applications, Vol. 16, Issue. 11, p. 1257.

Tang, X. H. and Lin, Xiaoyan 2011. Existence and multiplicity of homoclinic solutions for second-order discrete Hamiltonian systems with subquadratic potential. Journal of Difference Equations and Applications, Vol. 17, Issue. 11, p. 1617.

Lin, Xiaoyan and Tang, X.H. 2011. Existence of infinitely many homoclinic orbits in discrete Hamiltonian systems. Journal of Mathematical Analysis and Applications, Vol. 373, Issue. 1, p. 59.

Tan, Wei Ming and Su, Fang 2011. Existence of Periodic Solutions for a Class of Second-Order Nonlinear Difference Systems. Applied Mechanics and Materials, Vol. 148-149, Issue. , p. 1164.

Anderson, Douglas R. and Avery, Richard I. 2011. Existence of a periodic solution for continuous and discrete periodic second-order equations with variable potentials. Journal of Applied Mathematics and Computing, Vol. 37, Issue. 1-2, p. 297.

He, Tieshan Lu, Yimin Lei, Youfa Yang, Fengjian and Du, Zengji 2011. Nontrivial Periodic Solutions for Nonlinear Second‐Order Difference Equations. Discrete Dynamics in Nature and Society, Vol. 2011, Issue. 1,

He, Xiaofei and Chen, Peng 2011. Homoclinic solutions for second order discrete p-Laplacian systems. Advances in Difference Equations, Vol. 2011, Issue. 1,

Chen, Peng and Tang, X.H. 2011. Existence of infinitely many homoclinic orbits for fourth-order difference systems containing both advance and retardation. Applied Mathematics and Computation, Vol. 217, Issue. 9, p. 4408.

Download full list

Article contents

PERIODIC SOLUTIONS OF SECOND ORDER SELF-ADJOINT DIFFERENCE EQUATIONS

Abstract

Keywords

Access options

Footnotes

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Article contents

PERIODIC SOLUTIONS OF SECOND ORDER SELF-ADJOINT DIFFERENCE EQUATIONS

Abstract

Keywords

Access options

Footnotes

Save article to Kindle

Save article to Dropbox

Save article to Google Drive

Reply to: Submit a response

Your details

You have entered the maximum number of contributors

Conflicting interests