差分方程解的稳定性、有界性及概周期解的存在性

Abstract

Abstract: By using Liapunov function, the author establishes sufficient and necessary conditions for the uniform stability, uniformly asymptotic stability and exponential stability of solutions for a high dimension difference equation. Moreover, the author also proves that the uniformly asymptotic stability implies the boundedness of solutions. A sufficient condition is given for the
existence and uniformly asymptotic stability of almost periodic solutions for almost periodic difference equations.

Key words: Difference equation, Stability, Boundedness, Almost periodicity, Liapunov function

CLC Number:

34K45

Yang Xitao. Stability and Boundedness of Solutions and Existence of Almost Periodic Solution for Difference Equations[J].Acta mathematica scientia,Series A, 2008, 28(5): 870-878.

Trendmd

[1]	Gu Haibo, Gao Caixia. Razumikhin-Type Theorems on P-th Moment and Almost Sure Stability of Neutral Stochastic Switched Nonlinear Systems [J]. Acta mathematica scientia,Series A, 2018, 38(5): 970-983.
[2]	Zheng Lifei, Guo Jie, Wu Meihua, Wang Xiaorui, Wan Aying. The Research on a Class of the Predator-Prey-Mutualist System with Delays [J]. Acta mathematica scientia,Series A, 2018, 38(5): 1001-1013.
[3]	Wu Bin, Gao Ying, Yan Lin, Yu Jun. Carleman Estimate for a 2×2 Strongly Coupled Partial Differential System with Nonsingular Coefficient Matrix of Principal Parts and Application to an Inverse Source Problem [J]. Acta mathematica scientia,Series A, 2018, 38(4): 779-799.
[4]	Wang Junli, Zhang Xingwei, Liu Jian. Instability of Plane Couette-Poiseuille Flow of Compressible Navier-Stokes Equation [J]. Acta mathematica scientia,Series A, 2018, 38(2): 322-333.
[5]	Wang Wansheng, Zhong Peng, Zhao Xinyang. Long-Time Stability of Nonlinear Neutral Differential Equations with Variable Delay [J]. Acta mathematica scientia,Series A, 2018, 38(1): 96-109.
[6]	Li Haixia. Stability and Uniqueness of Positive Solutions for a Food-Chain Model [J]. Acta mathematica scientia,Series A, 2017, 37(6): 1094-1104.
[7]	Meng Xiaoying. Analysis of a Stochastic Delayed Epidemic Model with a Non-Monotonic Incidence Rate [J]. Acta mathematica scientia,Series A, 2017, 37(6): 1162-1175.
[8]	Wang Chun, Xu Tianzhou. Solution and Hyers-Ulam-Rassias Stability of a Mixed Type Quadratic-Additive Functional Equation with a Parameter in Quasi-Banach Spaces [J]. Acta mathematica scientia,Series A, 2017, 37(5): 846-859.
[9]	Chen Hongbin, Gan Siqing, Xu Da, Peng Yulong. A Formally Second-Order BDF Compact ADI Difference Scheme for the Two-Dimensional Fractional Evolution Equation [J]. Acta mathematica scientia,Series A, 2017, 37(5): 976-992.
[10]	Gao Hongya, Jia Miaomiao. Local Regularity and Local Boundedness for Solutions to Obstacle Problems [J]. Acta mathematica scientia,Series A, 2017, 37(4): 706-713.
[11]	Yang Jihua, Zhang Erli, Liu Mei. Dynamic Analysis and Chaos Control of a Finance System with Delayed Feedbacks [J]. Acta mathematica scientia,Series A, 2017, 37(4): 767-782.
[12]	Xiong Jun, Li Junmin, He Chao. Fuzzy Boundary Control Design for a Class of First-Order Hyperbolic PDEs [J]. Acta mathematica scientia,Series A, 2017, 37(3): 469-477.
[13]	Wei Aiju, Zhang Xinjian, Wang Junyi, Li Kezan. Dynamics Analysis of an Ebola Epidemic Model [J]. Acta mathematica scientia,Series A, 2017, 37(3): 577-592.
[14]	Wang Wei, Zhu Yucan. Stability of Fusion Frame Systems under Perturbation of the Local Frame Vectors [J]. Acta mathematica scientia,Series A, 2017, 37(2): 228-238.
[15]	Wang Xuewu. Convergence and Stability of Ishikawa Type Iterative Sequences for the φ-Hemi Pseudocontractive Operator Pair [J]. Acta mathematica scientia,Series A, 2017, 37(2): 248-256.

Stability and Boundedness of Solutions and Existence of Almost Periodic Solution for Difference Equations

PDF (PC)

Abstract

Cite this article

share this article

References

Related Articles 15

Metrics

Comments

Recommended 10