Abstract:
By the direct Lyapunov method we prove a sufficient condition for the exponential dichotomy with weakened (in comparison with a case of arbitrary coefficients) requirements to the difference derivative of the Lyapunov function along the system trajectory. We give an illustrating example.
Keywords:
exponential dichotomy, indefinite Hermitian form, shell of an almost periodical matrix.
Citation:
R. K. Romanovskii, L. V. Belgart, “The exponential dichotomy of solutions to systems of linear difference equations with almost periodic coefficients”, Izv. Vyssh. Uchebn. Zaved. Mat., 2010, no. 10, 51–59; Russian Math. (Iz. VUZ), 54:10 (2010), 44–51
\Bibitem{RomBel10}
\by R.~K.~Romanovskii, L.~V.~Belgart
\paper The exponential dichotomy of solutions to systems of linear difference equations with almost periodic coefficients
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2010
\issue 10
\pages 51--59
\mathnet{http://mi.mathnet.ru/ivm7139}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2808741}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2010
\vol 54
\issue 10
\pages 44--51
\crossref{https://doi.org/10.3103/S1066369X10100051}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-78649531996}
Linking options:
https://www.mathnet.ru/eng/ivm7139
https://www.mathnet.ru/eng/ivm/y2010/i10/p51
This publication is cited in the following 11 articles:
Petr Hasil, Michal Veselý, “Limit periodic perturbations of difference systems with coefficients from commutative groups”, Journal of Difference Equations and Applications, 29:1 (2023), 43
Hasil P., Vesely M., “Asymptotically Almost Periodic Solutions of Limit Periodic Difference Systems With Coefficients From Commutative Groups”, Topol. Methods Nonlinear Anal., 54:2 (2019), 515–535
Hasil P., Vesely M., “Solution Spaces of Homogeneous Linear Difference Systems With Coefficient Matrices From Commutative Groups”, J. Differ. Equ. Appl., 23:8 (2017), 1324–1353
V. E. Slyusarchuk, “Almost-periodic solutions of discrete equations”, Izv. Math., 80:2 (2016), 403–416
Romanovskii R.K., Nazaruk E.M., “Dichotomy of Solutions of Functional-Differential Equations in the Sobolev Space”, Differ. Equ., 51:4 (2015), 464–476
Hasil P., Vesely M., “Limit Periodic Homogeneous Linear Difference Systems”, Appl. Math. Comput., 265 (2015), 958–972
Chvatal M., “Asymptotically Almost Periodic Solutions of Limit and Almost Periodic Linear Difference Systems”, Electron. J. Qual. Theory Differ., 2015, no. 75
Chvatal M., “Non-Almost Periodic Solutions of Limit Periodic and Almost Periodic Homogeneous Linear Difference Systems”, Electron. J. Qual. Theory Differ., 2014, no. 76, 1–20
Hasil P., Vesely M., “Limit Periodic Linear Difference Systems With Coefficient Matrices From Commutative Groups”, Electron. J. Qual. Theory Differ., 2014, no. 23, 1–25
Hasil P., Vesely M., “Almost periodic transformable difference systems”, Applied Mathematics and Computation, 218:9 (2012), 5562–5579
Nazaruk E.M., Romanovskaya A.M., “Ob eksponentsialnoi dikhotomii reshenii zadachi koshi dlya sistemy differentsialno-raznostnykh uravnenii s postoyannymi koeffitsientami”, Vestnik omskogo universiteta, 2011, no. 4, 45–49
On the exponential dichotomy of cauchy problem solutions for systems of difference-differential equations with constant coefficients
Citation in format AMSBIB
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