A nonlinear Volterra equation with rapidly decaying solutions

Staffans, Olof J.

doi:10.1090/S0002-9947-1980-0558188-X

A nonlinear Volterra equation with rapidly decaying solutions
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by Olof J. Staffans

Trans. Amer. Math. Soc. 258 (1980), 523-530

DOI: https://doi.org/10.1090/S0002-9947-1980-0558188-X

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Abstract:

We study the asymptotic behavior of the solutions of a nonlinear integrodifferential Volterra equation with a convolution kernel. More specifically, we give conditions which imply that a solution x satisfies $x(t) = O({t^{ - p}}) (t \to \infty )$, where p is an arbitrary, positive real number.

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