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Ukrainian Mathematical Journal

, Volume 51, Issue 12, pp 1875–1891 | Cite as

Essentially unstable solutions of difference equations

  • V. E. Slyusarchuk
Article

Abstract

We study the essential instability of solutions of linear and nonlinear difference equations.

Keywords

Difference Equation Trivial Solution Essential Spectrum Finite Rank Linear Continuous Operator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    V. Yu. Slyusarchuk, “Essentially unstable solutions of difference equations,”Dop. Akad. Nauk Ukr., No. 7, 9–12 (1996).Google Scholar
  2. 2.
    R. R. Akhmerov, M. I. Kamenskii, A. S. Potapov, A. E. Rodkina, and B. N. Sadovskii,Measures of Noncompactness and Condensing Operators [in Russian], Nauka, Novosibirsk (1986).zbMATHGoogle Scholar
  3. 3.
    P. Clément, H. Heijmans, S. Angenent, C. van Duijn, and B. de Pagter,One-Parameter Semigroups [Russian translation], Mir, Moscow (1992).Google Scholar
  4. 4.
    V. E. Slyusarchuk, “Theorems on instability of systems with respect to linear approximation,”Ukr. Mat. Zh.,48, No. 8, 1104–1113 (1996).CrossRefMathSciNetGoogle Scholar
  5. 5.
    V. Rakocevic, “On the subset of M. Scheckter’s essential spectrum,”Mat. Vesnik,5, No. 4, 389–391 (1981).MathSciNetGoogle Scholar
  6. 6.
    V. Rakocevic, “On the essential approximate point spectrum. II,”Mat. Vesnik,36, No. 1, 89–97 (1984).zbMATHMathSciNetGoogle Scholar
  7. 7.
    T. Kato,Perturbation Theory for Linear Operators [Russian translation], Mir, Moscow (1972).zbMATHGoogle Scholar
  8. 8.
    N. Dunford and J. Schwartz,Linear Operators, Part II:Spectral Theory, Self-Adjoint Operators in Hilbert Space, Wiley, New York (1963).Google Scholar
  9. 9.
    M. Reed and B. Simon,Methods of Modern Mathematical Physics I: Functional Analysis, Academic Press, New York (1974).Google Scholar
  10. 10.
    V. A. Erovenko,Spectral and Fredholm Properties of Linear Operators in Banach Spaces [in Russian], Doctoral-Degree Thesis (Physics and Mathematics), Minsk (1995).Google Scholar
  11. 11.
    V. E. Slyusarchuk, “Difference equations in functional spaces,” in: D. I. Martynyuk,Lectures on Qualitative Theory of Difference Equations [in Russian], Naukova Dumka, Kiev (1972), pp. 197–222.Google Scholar
  12. 12.
    V. E. Slyusarchuk, “New theorems on instability of difference systems with respect to the first approximation,”Differents. Uravn.,19, No. 5, 906–908 (1983).zbMATHMathSciNetGoogle Scholar
  13. 13.
    V. E. Slyusarchuk, “Instability of difference equations with respect to the first approximation,”Differents. Uravn.,22, No. 4, 722–723 (1986).zbMATHMathSciNetGoogle Scholar
  14. 14.
    V. E. Slyusarchuk, “Instability of autonomous systems with respect to the linear approximation,” in:Asymptotic Methods and Their Application to Problems of Mathematical Physics [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1990), pp. 112–114.Google Scholar
  15. 15.
    A. I. Markushevich,A Short Course on the Theory of Analytic Functions [in Russian], Nauka, Moscow (1966).Google Scholar
  16. 16.
    R. Bellman and K. Cooke,Difference-Differential Equations [Russian translation], Mir, Moscow (1967).Google Scholar
  17. 17.
    A. N. Kolmogorov and S. V. Fomin,Elements of the Theory of Functions and Functional Analysis [in Russian], Nauka, Moskow (1968).Google Scholar

Copyright information

© Kluwer Academic/Plenum Publishers 2000

Authors and Affiliations

  • V. E. Slyusarchuk
    • 1
  1. 1.Rovno Technical UniversityRovno

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