Mathematics

Existence of anti-periodic solutions for a class of nonlinear discrete dynamical systems

  • Xin MENG
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  • College of Mathematics, Jilin Normal University, Siping, Jilin 136000, China

Received date: 2021-03-23

  Online published: 2022-11-22

Abstract

This paper explores the existence of anti-periodic solutions for a class of nonlinear discrete dynamical systems with summable dichotomy. Using the Banach fixed-point theorem, sufficient conditions for the existence and uniqueness of anti-periodic solutions for nonlinear discrete dynamical systems are established. Lastly, an example is presented to illustrate the main results.

Cite this article

Xin MENG . Existence of anti-periodic solutions for a class of nonlinear discrete dynamical systems[J]. Journal of East China Normal University(Natural Science), 2022 , 2022(6) : 38 -43 . DOI: 10.3969/j.issn.1000-5641.2022.06.005

References

1 AGARWAL R P, CABADA A, OTERO-ESPINAR V, et al. Existence and uniqueness of solutions for anti-periodic difference equations. Archives of Inequalities and Applications, 2004, 2 (4): 397- 412.
2 XU C J, ZHANG Q M. Anti-periodic solutions for a shunting inhibitory cellular neural networks with distributed delays and time-varying delays in the leakage terms. WSEAS Transactions on Mathematics, 2014, 13 (2): 736- 746.
3 LIU Y J. Anti-periodic boundary value problems for nonlinear higher order functional difference equations. Journal of Mathematical Inequalities, 2007, (3): 409- 417.
4 孟鑫. 一类非线性离散扰动系统的反周期解. 华东师范大学学报(自然科学版), 2019, (6): 1- 6.
5 CHOW S N, LEIVA H. Existence and roughness of the exponential dichotomy for skew-product semiflows in Banach spaces. Journal of Differential Equations, 1995, 120 (2): 429- 477.
6 PINTO M. Dichotomy and existence of periodic solutions of quasilinear functional differential equations. Nonlinear Analysis, 2010, 72 (3): 1227- 1234.
7 BEREZANSKY L, BRAVERMAN E. On exponential dichotomy, Bohl-Perron type thorems and stability of difference equations. Journal of Mathematical Analysis and Applications, 2005, 304 (2): 511- 530.
8 KOYUNCUOLU H C, ADIVAR M. On the affine-periodic solutions of discrete dynamical systems. Turkish Journal of Mathematics, 2018, 42 (5): 2260- 2269.
9 ZHANG J M, FAN M, ZHU H P. Existence and roughness of exponential dichotomies of linear dynamic equations on time scales. Computers & Mathematics with Applications, 2010, 59 (8): 2658- 2675.
10 PINTO M. Weighted convergent and bounded solutions of difference systems. Computers & Mathematics with Applications, 1998, 36 (10/11/12): 391- 400.
11 CUEVAS C, PINTO M. Convergent solutions of linear functional difference equations in phase space. Journal of Mathematical Analysis and Applications, 2003, 277 (1): 324- 341.
12 CAMPO L D, PINTO M, VIDAL C. Bounded and periodic solutions in retarded difference equations using summable dichotomies. Dynamic Systems and Applications, 2012, 21, 1- 15.
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