Abstract
We establish efficient conditions sufficient for the unique solvability of certain classes of Cauchy problems for systems of linear functional-differential equations. The conditions obtained are optimal in a certain sense.
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REFERENCES
E. Bravyi R. Hakl A. Lomtatidze (2002) ArticleTitleOptimal conditions for unique solvability of the Cauchy problem for first order linear functional differential equations Czech. Math. J. 52 IssueID3 513–530
R. Hakl A. Lomtatidze B. PůŽa (2001) ArticleTitleOn nonnegative solutions of first order scalar functional differential equations Mem. Differ. Equ. Math. Phys. 23 51–84
A. N. Ronto (2003) ArticleTitleExact solvability conditions for the Cauchy problem for systems of first-order linear functional-differential equations determined by ( σ1, σ2,..., σn; τ)-positive operators Ukr. Mat. Zh. 55 IssueID11 1541–1568
M. G. Krein M. A. Rutman (1948) ArticleTitleLinear operators leaving invariant a cone in a Banach space Usp. Mat. Nauk 3 IssueID1(23) 3–95
M. A. Krasnosel’skii G. M. Vainikko P. P. Zabreiko Y. B. Rutitskii V. Y. Stetsenko (1969) Approximate Solution of Operator Equations Nauka Moscow
N. V. Azbelev V. P. Maksimov L. F. Rakhmatullina (1991) Introduction to the Theory of Functional Differential Equations Nauka Moscow
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 56, No. 7, pp. 867–884, July, 2004.
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Dil’naya, N.Z., Ronto, A.N. Some new conditions for the solvability of the cauchy problem for systems of linear functional-differential equations. Ukr Math J 56, 1033–1053 (2004). https://doi.org/10.1007/PL00022171
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DOI: https://doi.org/10.1007/PL00022171