Positive definite measures with applications to a Volterra equation
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- by Olof J. Staffans PDF
- Trans. Amer. Math. Soc. 218 (1976), 219-237 Request permission
Abstract:
We study the asymptotic behavior of the solutions of the nonlinear Volterra integrodifferential equation \begin{equation}\tag {$\ast $} x’(t) + \int _0^t {g(x(t - \tau ))\;d\mu (\tau ) = f(t),}\end{equation} with a positive definite kernel $\mu$. In particular, we give new sufficient conditions on the kernel $\mu$, which together with standard assumptions on f and g yield results on boundedness and asymptotic behavior of the solutions of $(\ast )$. Our proofs are based on the theory of distribution Fourier transforms.References
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Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 218 (1976), 219-237
- MSC: Primary 45D05; Secondary 45M05, 42-XX
- DOI: https://doi.org/10.1090/S0002-9947-1976-0458086-5
- MathSciNet review: 0458086