一类变指数二阶差分系统的周期解

doi:10.13438/j.cnki.jdzk.2026.01.001

吉首大学学报（自然科学版） ›› 2026, Vol. 47 ›› Issue (1): 1-5.DOI: 10.13438/j.cnki.jdzk.2026.01.001

• 数学 • 下一篇

一类变指数二阶差分系统的周期解

张申贵

（西北民族大学数学与计算机科学学院，甘肃兰州 730030）

出版日期:2026-01-25 发布日期:2026-01-30
作者简介:张申贵(1980—),男,甘肃兰州人,西北民族大学数学与计算机科学学院副教授,博士,主要从事非线性泛函分析研究.
基金资助:
国家自然科学基金资助项目(12361047)；中央高校基本科研业务费资助项目(31920240091)

Periodic Solutions for a Class of Second-Order Difference Systems with Variable Exponent

ZHANG Shengui

（College of Mathematics and Computer Science，Northwest Minzu University,Lanzhou 730030,China）

Online:2026-01-25 Published:2026-01-30

摘要/Abstract

摘要：探究了离散p(k)-Laplace系统周期边值问题解的存在性. 在一类广义次二次条件下，利用鞍点定理获得了周期解的存在性结果，并举例说明了可解性条件的有效性.

关键词： 差分系统, 变指数, 临界点, 周期解

Abstract: This paper investigates the existence of solutions for periodic boundary value of discrete p(k)-Laplacian systems.Under the generalized subquadratic conditions,some results for the existence of periodic solutions are obtained by using the saddle point theorem,and the validity of the solvability conditions is proved.

Key words: difference systems, variable exponent, critical point, periodic solution

张申贵. 一类变指数二阶差分系统的周期解[J]. 吉首大学学报（自然科学版）, 2026, 47(1): 1-5.

ZHANG Shengui. Periodic Solutions for a Class of Second-Order Difference Systems with Variable Exponent[J]. Journal of Jishou University(Natural Sciences Edition), 2026, 47(1): 1-5.

参考文献

[1] ZHIKOV VASILIJ.On Some Variational Problems[J].Russian Journal of Mathematical Physics,1997,5(1):105-116.
[2] AUTUORI GIUSEPPINA,PUCCI PATRIZIA,SALVATORI MARIA.Asymptotic Stability for Anisotropic Kirchhoff Systems[J].Journal of Mathematical Analysis and Applications,2009,352(1):149-165.
[3] GUO Zhiming,YU Jianshe.The Existence of Periodic and Subharmonic Solutions of Subquadratic Second Order Difference Equations[J].Journal of the London Mathematical Society,2003,68(2):419-430.
[4] BALANOV ZALMAN,CARLOS GARCIA,KRAWCEWICZ WIESLAW.On Variational and Topological Methods in Nonlinear Difference Equations[J].Communications on Pure and Applied Analysis,2018,17(6):2813-2844.
[5] DING Liang,WEI Jinlong.Notes on Nontrivial Multiple Periodic Solutions for Second-Order Discrete Hamiltonian Systems[J].Bulletin of the Malaysian Sciences Society,2020,43(1):4393-4409.
[6] ZHOU Benxing,LIU Chungen.Applications of Conley Index Theory on Difference Equations with Non-Resonance[J].Applied Mathematics Letters,2020,108(1):1-6.
[7] LIU Chungen,ZHONG Yuyou.Existence and Multiplicity of Periodic Solutions for Nonautonomous Second Order Discrete Hamiltonian Systems[J].Constructive Mathematical Analysis,2020,3(4):178-188.
[8] MAWHIN JEAN,WILLEM MICHEL.Critical Point Theory and Hamiltonian Systems[M].New York:Springer Verlag,1989：85-91.
[9] BEREANU CRISTIAN,JEBELEAN PETRU,SERBAN CALIN.Periodic and Neumann Problems for Discrete P(·)-Laplacian[J].Journal of Mathematical Analysis and Applications,2013,399(1):75-87.
[10] ZHANG Shengui.Periodic Solutions for Discrete P(k)-Laplacian Systems with Partially Periodic Potential[J].Advances in Difference Equtions,2018,242:1-15.
[11] 张申贵.变指数二阶差分系统的非平凡周期解[J].应用数学,2021,34(4):847-854.
[12] 张申贵.一类变指数离散二阶系统的周期解[J].中山大学学报(自然科学版),2022,61(2):163-170.
[13] TANG Chunlei,WU Xingping.Notes on Periodic Solutions of Subquadratic Second Order Systems[J].Journal of Mathematical Analysis and Applications,2003,285(1):8-16.

一类变指数二阶差分系统的周期解

Periodic Solutions for a Class of Second-Order Difference Systems with Variable Exponent

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