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Biletskyi, B. A.; Boichuk, A. A.; Pokutnyi, A. A.

Periodic problems of difference equations and ergodic theory. (English) Zbl 1222.34074

Abstr. Appl. Anal. 2011, Article ID 928587, 12 p. (2011).
Summary: Necessary and sufficient conditions for solvability of a family of difference equations with periodic boundary condition were obtained using the notion of relative spectrum of a linear bounded operator in the Banach space and an ergodic theorem. It is shown that when the condition of existence is satisfied, then such periodic solutions are built using the formula for the generalized inverse operator to the linear limited one.

Cited in 3 Documents

MSC:

34K10 Boundary value problems for functional-differential equations
34K13 Periodic solutions to functional-differential equations
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\textit{B. A. Biletskyi} et al., Abstr. Appl. Anal. 2011, Article ID 928587, 12 p. (2011; Zbl 1222.34074)
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References:

[1] B. P. Demidovich, Lectures Mathematical Theory of Stability, Nauka, Moscow, Russia, 1967. · Zbl 0155.41601
[2] Y. L. Daletskyi and M. G. Krein, Stability of Solutions of Differential Equations in Banach Space, Nauka, Moscow, Russia, 1970.
[3] A. A. Boichuk and A. M. Samoilenko, Generalized Inverse Operators and Fredholm Boundary Value Problems, VSP, Utrecht, The Netherlands, 2004. · Zbl 1083.47003
[4] I. D. Chueshov, Introduction to the Theory of Infinite-Dimensional Dissipative Systems, ACTA, Kharkov, Ukraine, 2002. · Zbl 1100.37047
[5] A. A. Boichuk and A. A. Pokutnyi, “Criterion of solvability of difference equations in Banach space,” in Bulgarian-Turkish-Ukrainian Scientific Conference Mathematical Analysis, Differential Equations and Their Applications, pp. 241-247, Prof. Marin Drinov Academic Publishing House, Sunny Beach, Bulgaria, September 2010.
[6] K. Iosida, Functional Analysis, Springer, Berlin, Germany, 1965.
[7] E. H. Moore, “On the reciprocal of the general algebraic matrix (Abstract),” Bulletin of the American Mathematical Society, no. 26, pp. 394-395, 1920.
[8] R. Penrose, “A generalized inverse for matrices,” Mathematical Proceedings of the Cambridge Philosophical Society, vol. 51, no. 3, pp. 406-413, 1955. · Zbl 0065.24603
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