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On Splitting with Different Growth Rates for Linear Discrete-Time Systems in Banach Spaces

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Difference Equations, Discrete Dynamical Systems and Applications (ICDEA 2017)

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Abstract

The aim of this work is to study a property of trisplitting with different growth rates for linear discrete-time systems in Banach spaces. Some characterizations for this concept are given and as consequences, we obtain some results for exponential trisplitting and for the trichotomy with different growth rates, particularly for exponential trichotomy.

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References

  1. Aulbach, B., Kalkbrenner, J.: Exponential forward splitting for noninvertible difference equations. Comput. Math. Appl. 42, 743–754 (2001)

    Article  MathSciNet  Google Scholar 

  2. Aulbach, B., Siegmund, S.: The dichotomy spectrum for noninvertible systems of difference equations. J. Differ. Equ. Appl. 7, 895–913 (2001)

    Article  MathSciNet  Google Scholar 

  3. Barbashin, E.A.: Introduction to Stability Theory. Nauka, Moscow (1967)

    Google Scholar 

  4. Barreira, L., Valls, C.: Robustness of dichotomies and trichotomies for difference equations. Port. Math. 71(3/4), 277–300 (2014)

    Article  MathSciNet  Google Scholar 

  5. Coffman, C.V.: Asymptotic behavior of solutions of ordinary difference equations. Trans. Am. Math. Soc. 110, 22–51 (1964)

    Article  MathSciNet  Google Scholar 

  6. Cuevas, C., Vidal, C.: Weighted exponential trichotomy of linear difference equations. Dyn. Contin. Discret. Impuls. Syst. Ser. A 15, 353–379 (2008)

    Google Scholar 

  7. Elaydi, S., Hájek, O.: Some Remarks on Nonlinear Dichotomy and Trichotomy. Lecture Notes in Pure Mathematics, vol. 109, pp. 175–178 (1987)

    Google Scholar 

  8. Elaydi, S., Hájek, O.: Exponential trichotomy of differential systems. J. Math. Anal. Appl. 129, 362–374 (1988)

    Article  MathSciNet  Google Scholar 

  9. Elaydi, S., Hájek, O.: Exponential dichotomy and trichotomy of nonlinear differential equations. Differ. Integral Equ. 3, 1201–1224 (1990)

    MathSciNet  MATH  Google Scholar 

  10. Elaydi, S., Janglajew, K.: Dichotomy and trichotomy of difference equations. J. Differ. Equ. Appl. 3, 417–448 (1998)

    Article  MathSciNet  Google Scholar 

  11. Jiang, Y.: Robustness of a nonuniform \((\mu, \nu )\) trichotomy in Banach spaces. Electron. J. Differ. Equ. 154, 1–11 (2012)

    Google Scholar 

  12. Li, T.: Die stabilittsfrage bei differenzengleichungen. Acta Math. 63, 99–141 (1934)

    Article  MathSciNet  Google Scholar 

  13. L\(\acute{o}\)pez-Fenner, J., Pinto, M.: \((h,k)\)-Trichotomies and asymptotics of nonautonomous difference systems. Comput. Math. Appl. 33, 105–124 (1997)

    Google Scholar 

  14. Megan, M., Popa, I.L.: Exponential splitting for nonautonomous linear discrete-time systems in Banach spaces. J. Comput. Appl. Math. 312, 181–191 (2017)

    Article  MathSciNet  Google Scholar 

  15. Mihiţ, C.L., Borlea, D., Megan, M.: On some concepts of \((h,k)\)-splitting for skew-evolution semiflows in Banach spaces. Ann. Acad. Roman. Sci. Ser. Math. Appl. 9(2), 186–204 (2017)

    Google Scholar 

  16. Mihiţ, C.L., Megan, M., Ceauşu, T.: The equivalence of Datko and Lyapunov properties for \((h,k)\)-trichotomic linear discrete-time systems. Discrete Dyn. Nat. Soc. vol. 2016, 8. Article ID 3700262

    Google Scholar 

  17. Popa, I.L., Megan, M., Ceauşu, T.: Exponential dichotomies for linear discrete-time systems in Banach spaces. Appl. Anal. Discrete Math. 6, 140–155 (2012)

    Article  MathSciNet  Google Scholar 

  18. Pötzsche, C.: Geometric Theory of Discrete Nonautonomous Dynamical Systems. Lecture Notes in Mathematics, vol. 2002. Springer (2010)

    Google Scholar 

  19. Pötzsche, C.: Fine structure of the dichotomy spectrum. Integr. Equ. Oper. Theory 73, 107–151 (2012)

    Google Scholar 

  20. Przyluski, K.M., Rolewicz, S.: On stability of linear time-varying infinit-dimensional discrete-time systems. Syst. Control Lett. 4, 307–315 (1984)

    Article  Google Scholar 

  21. Sacker, R.J., Sell, G.R.: Existence of dichotomies and invariant splittings for linear differential systems, III. J. Differ. Equ. 22, 497–522 (1976)

    Article  MathSciNet  Google Scholar 

  22. Sasu, A.L., Sasu, B.: Exponential trichotomy for variational difference equations. J. Differ. Equ. Appl. 15, 693–718 (2009)

    Article  MathSciNet  Google Scholar 

  23. Sasu, A.L., Sasu, B.: Input-output admissibility and exponential trichotomy of difference equations. J. Math. Anal. Appl. 380, 17–32 (2011)

    Article  MathSciNet  Google Scholar 

  24. Sasu, A.L., Sasu, B.: Discrete admissibility and exponential trichotomy of dynamical systems. Discrete Contin. Dyn. Syst. 34(7), 2929–2962 (2014)

    Article  MathSciNet  Google Scholar 

  25. Zabczyk, J.: Remarks on the control of discrete-time distributed parameter systems. SIAM J. Control 12, 721–735 (1974)

    Article  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Academy of Romanian Scientists, Splaiul Independenţei 54, 050094, Bucharest, Romania

    Mihail Megan

  2. Faculty of Mathematics and Computer Science, Department of Mathematics, West University of Timişoara, V. Pârvan Blv. No. 4, 300223, Timişoara, Romania

    Claudia Luminiţa Mihiţ

  3. Faculty of Economic Sciences, Eftimie Murgu University, Traian Vuia No. 1-4, Reşiţa, Romania

    Raluca Lolea

Authors
  1. Mihail Megan
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  2. Claudia Luminiţa Mihiţ
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  3. Raluca Lolea
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Corresponding author

Correspondence to Mihail Megan .

Editor information

Editors and Affiliations

  1. Department of Mathematics, Trinity University, San Antonio, TX, USA

    Saber Elaydi

  2. Institut für Mathematik, Alpen-Adria Universität Klagenfurt, Klagenfurt, Austria

    Christian Pötzsche

  3. Department of Mathematics, West University of Timişoara, Timişoara, Romania

    Adina Luminiţa Sasu

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Megan, M., Mihiţ, C.L., Lolea, R. (2019). On Splitting with Different Growth Rates for Linear Discrete-Time Systems in Banach Spaces. In: Elaydi, S., Pötzsche, C., Sasu, A. (eds) Difference Equations, Discrete Dynamical Systems and Applications. ICDEA 2017. Springer Proceedings in Mathematics & Statistics, vol 287. Springer, Cham. https://doi.org/10.1007/978-3-030-20016-9_15

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