研究了一类具有指数型二分性非线性离散扰动系统的反周期解.应用Banach不动点定理,给出了非线性离散扰动系统存在唯一反周期解的充分条件,并通过例子说明了主要结论在实际问题中的应用.
In this paper, anti-periodic solutions for a class of nonlinear discrete perturbed systems with exponential dichotomy are studied. By means of the Banach fixed point theorem, new sufficient conditions for the existence and uniqueness of anti-periodic solutions for nonlinear discrete perturbed systems are established. An example is given to illustrate the results we obtained.
[1] COPPEL W A. Dichotomies in Stability Theory[M]. New York:Springer-Verlag, 1978.
[2] CHURCH K, LIU X. Bifurcation of bounded solutions of impulsive differential equations[J]. International Journal of Bifurcation and Chaos, 2016, 26(14):1-20.
[3] PINTO M. Dichotomy and existence of periodic solutions of quasilinear functional differential equations[J]. Nonlinear Analysis, 2010, 72(3):1227-1234.
[4] RODRIGUES H M, SILVERIA M. On the relationship between exponential dichotomies and the Fredholm alternative[J]. J Differential Equations, 1988, 73(3):78-81.
[5] BEREZANSKY L, BRAVERMAN E. On exponential dichotomy, Bohl-Perron type thorems and stability of difference equations[J]. J Math Anal Appl, 2005, 304(2):511-530.
[6] DRAGICEVIC D. A note on the nonuniform exponential stability and dichotomy for nonautonomous difference equations[J]. Linear Algebra and Its Applications, 2018, 552(1):105-126.
[7] AULBACH B, MINH N. The concept of spctral dichotomy for linear difference equations[J]. J Math Anal Appl, 1994, 185(2):275-287.
[8] HUY N T, MINH N V. Exponential dichotomy of difference equations and applications to evolution equations on the half-line[J]. Computers & Mathematics with Applications, 2001, 42(3/5):301-311.
[9] ZHANG J, FAN M, ZHU H. Existence and roughness of exponential dichotomies of linear dynamic equations on time scales[J]. Computers & Mathematics with Applications, 2010, 59(8):2658-2675.
[10] AGARWAL R P, CABADA A, OTERO-ESPINAR V. Existence and uniqueness results for n-th order nonlinear difference equations in presence of lower and upper solutions[J]. Arch Inequal Appl, 2003, 1(3/4):421-431.
[11] AGARWAL R P, CABADA A, OTERO-ESPINAR V, et al. Existence and uniqueness of solutions for antiperiodic difference equations[J]. Arch Inequal Appl, 2004, 2(4):397-412.
[12] KUANG J, YANG Y. Variational approach to anti-periodic boundary value problems involving the discrete p-Laplacian[J]. Boundary Value Problems, 2018(1):86.
[13] LÜ X, YAN P, LIU D. Anti-periodic solutions for a class of nonlinear second-order Rayleigh equations with delays[J]. Commun Nonlinear Sci Numer Simul, 2010, 15(11):3593-3598.
[14] CHEN Y Q, CHO J, O'REGAN D. Anti-periodic solutions for evolution equations[J]. Math Nachr, 2005, 278(4):356-362.
[15] HADJIAN A, HEIDARKHANI S. Existence of one non-trivial anti-periodic solution for second-order impulsive differential inclusions[J]. Mathematical Methods in the Applied Science, 2017, 40(14):5009-5017.
[16] PU H, YANG J. Existence of anti-periodic solutions with symmetry for some high-order ordinary differential equations[J]. Boundary Value Problems, 2012(1):108.
[17] CHEN Z. Global exponential stability of anti-periodic solutions for neutral type CNNs with D operator[J]. International Journal of Machine Learning and Cybernetics, 2018, 9(7):1109-1115.