## On an asymptotic property of a Volterra integral equation

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- by A. F. Izé
- Proc. Amer. Math. Soc.
**28**(1971), 93-99 - DOI: https://doi.org/10.1090/S0002-9939-1971-0275078-0
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## 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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## Bibliographic 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