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Exact Solvability Conditions for the Cauchy Problem for Systems of First-Order Linear Functional-Differential Equations Determined by (σ1, σ2, ... , σ n ; τ)-Positive Operators

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Abstract

We obtain new sufficient conditions under which the Cauchy problem for a system of linear functional-differential equations is uniquely solvable for arbitrary forcing terms. The conditions established are unimprovable in a certain sense.

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REFERENCES

  1. N. V. Azbelev, V. P. Maksimov, and L. F. Rakhmatullina, Introduction to the Theory of Functional Differential Equations [in Russian], Nauka, Moscow (1991).

    Google Scholar 

  2. R. Hakl, A. Lomtatidze, and B. Půža, “On nonnegative solutions of first order scalar functional differential equations,” Mem. Different. Equat. Math. Phys., 23, 51–84 (2001).

    Google Scholar 

  3. I. A. Bakhtin, M. A. Krasnosel'skii, and V. Ya. Stetsenko, “On the continuity of linear positive operators,” Sib. Mat. Zh., 2, No. 1, 156–160 (1962).

    Google Scholar 

  4. M. A. Krasnosel'skii, Positive Solutions of Operator Equations, Noordhoff, Groningen (1964).

    Google Scholar 

  5. M. G. Krein and M. A. Rutman, “Linear operators leaving invariant a cone in a Banach space,” Usp. Mat. Nauk, 3, No. 1 (23), 3–95 (1948).

    Google Scholar 

  6. M. A. Krasnosel'skii, G. M. Vainikko, P. P. Zabreiko, Ya. B. Rutitskii, and V. Ya. Stetsenko, Approximate Solution of Operator Equations, Noordhoff, Groningen (1972).

  7. V. Ya. Stetsenko, “Criteria of indecomposability of linear operators,” Usp. Mat. Nauk, 21, No. 5, 265–266 (1966).

    Google Scholar 

  8. F. Riesz and B. Sz.-Nagy, Le Leçons d'Analyse Fonctionelle, Akadémiai Kiadó, Budapest (1955).

  9. B. Z. Vulikh, Introduction to the Theory of Semiordered Spaces [in Russian], Fizmatgiz, Moscow (1961).

  10. N. Dunford and J. T. Schwartz, Linear Operators. I. General Theory, Interscience, London (1958).

    Google Scholar 

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Authors and Affiliations

  1. Institute of Mathematics, Ukrainian Academy of Sciences, Kiev

    A. N. Ronto

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  1. A. N. Ronto
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Ronto, A.N. Exact Solvability Conditions for the Cauchy Problem for Systems of First-Order Linear Functional-Differential Equations Determined by (σ1, σ2, ... , σ n ; τ)-Positive Operators. Ukrainian Mathematical Journal 55, 1853–1884 (2003). https://doi.org/10.1023/B:UKMA.0000027047.61698.48

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  • DOI: https://doi.org/10.1023/B:UKMA.0000027047.61698.48

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