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Asymptotic Properties of Solutions to Systems of Nonlinear Functional-Differential Equations

Asymptotic Properties of Solutions to Systems of Nonlinear Functional-Differential Equations Differential Equations, Vol. 39, No. 1, 2003, pp. 46–50. Translated from Differentsial'nye Uravneniya, Vol. 39, No. 1, 2003, pp. 45–49. Original Russian Text Copyright c 2003 by Pelyukh. ORDINARY DIFFERENTIAL EQUATIONS Asymptotic Properties of Solutions to Systems of Nonlinear Functional-Di erential Equations G. P. Pelyukh Institute of Mathematics, National Academy of Sciences, Kiev, Ukraine Received November 15, 2001 1. Systems of nonlinear functional-di erential equations of the form 0 0 0 x (t +1) = x (t)+ F (t;x(t);x(f (t));x ('(t))) ; (1) + + n n n n + + + + where t 2 R =[0; +1), F : R  R  R  R ! R , f : R ! R , ' : R ! R , were studied by numerous mathematicians (e.g., see [1, 2]). Existence and uniqueness issues for various types of solutions satisfying some additional (initial or boundary) conditions have undergone especially comprehensive analysis [1{6]. Since in the general case, systems of the form (1) have solutions depending on arbitrary functions, it is natural to pose problems concerning the structure of solution sets of such equations. In the present paper, we consider the structure of the set of continuously di http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Differential Equations Springer Journals

Asymptotic Properties of Solutions to Systems of Nonlinear Functional-Differential Equations

Pelyukh, G.
Differential Equations , Volume 39 (1) – Oct 5, 2004
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References (3)

Publisher
Springer Journals
Copyright
Copyright © 2003 by MAIK “Nauka/Interperiodica”
Subject
Mathematics; Difference and Functional Equations; Ordinary Differential Equations; Partial Differential Equations
ISSN
0012-2661
eISSN
1608-3083
DOI
10.1023/A:1025163807158
Publisher site
See Article on Publisher Site

Abstract

Differential Equations, Vol. 39, No. 1, 2003, pp. 46–50. Translated from Differentsial'nye Uravneniya, Vol. 39, No. 1, 2003, pp. 45–49. Original Russian Text Copyright c 2003 by Pelyukh. ORDINARY DIFFERENTIAL EQUATIONS Asymptotic Properties of Solutions to Systems of Nonlinear Functional-Di erential Equations G. P. Pelyukh Institute of Mathematics, National Academy of Sciences, Kiev, Ukraine Received November 15, 2001 1. Systems of nonlinear functional-di erential equations of the form 0 0 0 x (t +1) = x (t)+ F (t;x(t);x(f (t));x ('(t))) ; (1) + + n n n n + + + + where t 2 R =[0; +1), F : R  R  R  R ! R , f : R ! R , ' : R ! R , were studied by numerous mathematicians (e.g., see [1, 2]). Existence and uniqueness issues for various types of solutions satisfying some additional (initial or boundary) conditions have undergone especially comprehensive analysis [1{6]. Since in the general case, systems of the form (1) have solutions depending on arbitrary functions, it is natural to pose problems concerning the structure of solution sets of such equations. In the present paper, we consider the structure of the set of continuously di

Journal

Differential Equations – Springer Journals

Published: Oct 5, 2004

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