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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On an asymptotic property of a Volterra integral equation
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by A. F. Izé PDF
Proc. Amer. Math. Soc. 28 (1971), 93-99 Request permission

Abstract:

It is proved that if $q(t - s)$ is bounded and $f(t,x)$ is “small,” the solutions of the integral equation $x(t) = a(t) + \int _0^t {q(t - s)f(s,x(s))ds}$ satisfies the conditions $x(t) = h(t) + \rho (t)a(t),{\lim _{t \to \infty }}a(t) = a$ constant where $\rho (t)$ is a nonsingular diagonal matrix chosen in such a way that $\rho (t)h(t)$ is bounded. The results are extended to the more general integral equation $x(t) = h(t) + \int _0^t {F(t,s,x(s))ds}$ and contain, in particular, some results on the boundedness, asymptotic behavior and existence of nonoscillatory solution of differential equations.
References
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Additional Information
  • © Copyright 1971 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 28 (1971), 93-99
  • MSC: Primary 45.13; Secondary 34.00
  • DOI: https://doi.org/10.1090/S0002-9939-1971-0275078-0
  • MathSciNet review: 0275078