On stability of difference equations in partially ordered spaces
Vestnik rossijskih universitetov. Matematika, Tome 23 (2018) no. 123, pp. 386-394 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider implicit difference equations in partially ordered spaces. We define the notion of a stable equilibrium point. The conditions of the stability is obtained. The study is based on the theory of partially ordered mappings.
Keywords: implicit difference equation, stable equilibrium point, partially ordered space, partially ordered mapping.
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T. V. Zhukovskaya; I. A. Zabrodskiy; M. V. Borzova. On stability of difference equations in partially ordered spaces. Vestnik rossijskih universitetov. Matematika, Tome 23 (2018) no. 123, pp. 386-394. http://geodesic.mathdoc.fr/item/VTAMU_2018_23_123_a5/

[1] S. Elaydi, An untroduction to difference equations, Springer-Verlag, New York, 2005, 540 pp. | MR

[2] E. Braverman, S. E. Zhukovskiy, “On stability and oscillation of equations with a distributed delay which can be reduced to difference equations”, Electronic Journal of Differential Equations, 2008, no. 112, 1–16 | MR

[3] A. V. Arutyunov, E. S. Zhukovskiy, S. E. Zhukovskiy, “Coincidence points principle for mappings in partially ordered spaces”, Topology and its Applications, 179:1 (2015), 13–33 | DOI | MR

[4] A. V. Arutyunov, E. S. Zhukovskiy, S. E. Zhukovskiy, “On coincidence points in partially ordered spaces”, Proceedings of the Russian Academy of Sciences, 453:5 (2013), 475–478 (In Russian)

[5] E. S. Zhukovskiy, “About orderly covering mappings and Chaplygin's type integral inequalities”, St. Petersburg Mathematical Journal, 30:1 (2018), 96–127 (In Russian)

[6] E. S. Zhukovskiy, “On ordered-covering mappings and implicit differential inequalities”, Differential Equations, 52:12 (2016), 1610–1627 (In Russian) | MR

[7] A. Arutyunov, S. Zhukovskiy, F. Pereira, “Solvability of implicit difference equations”, Lecture Notes in Electrical Engineering, 321 (2015), 23–28 | DOI

[8] S. E. Zhukovskiy, “Application of covering mappings to difference equations”, Tambov University Reports. Series: Natural and Technical Sciences, 16:4 (2011), 1085–1086 (In Russian)

[9] E. S. Zhukovskiy, I. A. Zabrodskiy, A. I. Shindyapin, “Periodic solutions of implicit differential equations”, Tambov University Reports. Series: Natural and Technical Sciences, 20:5 (2015), 1142–1146 (In Russian)

[10] I. A. Zabrodskiy, A. S. Kuzyakina, “Exponential stability of implicit difference equations”, Tambov University Reports. Series: Natural and Technical Sciences, 20:5 (2015), 1156–1160 (In Russian)

[11] A. V. Arutyunov, “Covering mappings in metric spaces and fixed points”, Proceedings of the Russian Academy of Sciences, 416:2 (2007), 151–155 (In Russian)

[12] E. R. Avakov, A. V. Arutyunov, E. S. Zhukovskiy, “Covering mappings and their applications to differential equations unsolved for the derivative”, Differential Equations, 45:5 (2009), 613–634 (In Russian) | MR

[13] A. V. Arutyunov, E. S. Zhukovskiy, S. E. Zhukovskiy, “Covering mappings and well-posedness of nonlinear Volterra equations”, Nonlinear Analysis: Theory, Methods and Applications, 75:3 (2012), 1026–1044 | DOI | MR

[14] A. V. Arutyunov, E. S. Zhukovskiy, S. E. Zhukovskiy, “On the well-posedness of differential equations unsolved for the derivative”, Differential Equations, 47:11 (2011), 1523–1537 (In Russian) | MR