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Periodica Mathematica Hungarica

, Volume 31, Issue 2, pp 97–103 | Cite as

On the rapidly decreasing solutions for some systems of differential equations with unbounded coefficients

  • Labib R. Awad
Article

Abstract

In this paper we continue the study of solvability of the non-homogeneous system of linear differential equations
$$y'(t) = C(t)y(t) + f(t),(y,f \in \mathbb{R}^n )$$
(1)
in the space of all rapidly decreasing functions, whereC(t) is a continuous square matrix of ordern for allt ∈ ℝ, whose elements are all unbounded functions on the real line ℝ. We give a necessary and sufficient condition in order that the system (1) be solvable in this space.

Mathematics subject classification numbers

1991. Primary 34A30 34C11 

Key words and phrases

Non-homogeneous system of linear differential equations rapidly decreasing functions 

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References

  1. [1]
    Labib R. Awad, On existence of bounded solutions for systems of homogeneous linear differential equations with unbounded coefficients.J. of Natural Sc. and Math. Vol.32, No.2 (1992), Lahore (Pakistan), 167–176.Google Scholar
  2. [2]
    Labib R. Awad, On the solvability of some systems of linear differential equations with unbounded coefficients, (under publication).Google Scholar
  3. [3]
    B. P. Demidovich,Lectures in the mathematical theory of stability, 1967 (in Russian).Google Scholar
  4. [4]
    V. C. Vladimirov,Equations of Mathematical Physics, Nauka, Moscow 1988 (in Russian).Google Scholar

Copyright information

© Akadémiai Kiadó 1995

Authors and Affiliations

  • Labib R. Awad
    • 1
  1. 1.Department of Mathematics Faculty of ScienceUniversity of Ain ShamsCairoEgypt

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