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Necessary and sufficient conditions for the lipschitzian invertibility of nonlinear difference operators in the spacesl p (ℤ, ℝ) with 1≤p≤∞with 1≤p≤∞

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Abstract

Necessary and sufficient conditions for the Lipschitzian invertibility of the difference map

$$(\mathcal{D}x)(n) = x(n + 1) - x(n) - f(x(n)), n \in \mathbb{Z},$$

, wheref: ℝ → ℝ is a continuous function, in the spacesl p (ℤ, ℝ), where 1≤p≤∞, of two-sided numerical sequences are obtained.

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References

  1. A. Halanay and D. Wexler,Teoria calitativă a sistemelor cu impulsuri, Editura Academici Republici Socialiste Rominia, Bucharest (1968).

    Google Scholar 

  2. D. I. Martynyuk,Lectures on the Qualitative Theory of Difference Equations [in Russian], Naukova Dumka, Kiev (1972).

    Google Scholar 

  3. V. G. Kurbatov,Linear Differential-Difference Equations [in Russian], Izd. Voronezh. Univ., Voronezh (1990).

    Google Scholar 

  4. A. Ya. Dorogovtsev,Periodic and Stationary Regimes of Infinite-Dimensional Determined and Stochastic Dynamical Systems [in Russian], Vishcha shkola, Kiev (1992).

    Google Scholar 

  5. S. V. Coffman and J. J. Schäffer, “Dichotomies for linear difference equations,”Math. Ann.,172, 139–166 (1967).

    Article  MATH  Google Scholar 

  6. V. E. Slyusarchuk, “On exponential dichotomy of solutions of discrete systems,”Ukrain. Mat. Zh. [Ukrainian Math. J.],35, No. 1, 109–115 (1983).

    Google Scholar 

  7. V. E. Slyusarchuk, “Invertibility of linear nonautonomous difference operators in the space of functions bounded onZ,”Mat. Zametki [Math. Notes],37, No. 5, 662–666 (1985).

    Google Scholar 

  8. V. E. Slyusarchuk, “On a representation of bounded solutions of linear discrete systems,”Ukrain. Mat. Zh. [Ukrainian Math. J.],39, No. 2, 210–215 (1987).

    MATH  Google Scholar 

  9. V. E. Slyusarchuk, “Weakly nonlinear perturbations of normally solvable functional-differential and discrete equations,”Ukrain. Mat. Zh. [Ukrainian Math. J.],39, No. 5, 660–662 (1987).

    MATH  Google Scholar 

  10. A. G. Baskakov, “Some conditions for the invertibility of linear differential and difference operators,”Dokl. Ross. Akad. Nauk [Russian Acad. Sci. Dokl. Math.],333, No. 3, 282–284 (1993).

    Google Scholar 

  11. A. N. Kolmogorov and S. V. Fomin,Elements of Function Theory and Functional Analysis [in Russian], Nauka, Moscow (1968).

    Google Scholar 

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Authors and Affiliations

  1. Rovno State Technical University, Rovno, USSR

    V. E. Slyusarchuk

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  1. V. E. Slyusarchuk
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Translated fromMatematicheskie Zametki, Vol. 68, No. 3, pp. 448–454, September, 2000.

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Slyusarchuk, V.E. Necessary and sufficient conditions for the lipschitzian invertibility of nonlinear difference operators in the spacesl p (ℤ, ℝ) with 1≤p≤∞with 1≤p≤∞. Math Notes 68, 386–391 (2000). https://doi.org/10.1007/BF02674563

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  • DOI: https://doi.org/10.1007/BF02674563

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