An integro-differential equation
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- by T. A. Burton PDF
- Proc. Amer. Math. Soc. 79 (1980), 393-399 Request permission
Abstract:
The vector equation \[ xโ(t) = A(t)x(t) + \int _0^t {C(t,s)D(x(s))x(s)ds + F(t)} \] is considered in which A is not necessarily a stable matrix, but $A(t) + G(t,t)D(0)$ is stable where G is an antiderivative of C with respect to t. Stability and boundedness results are then obtained. We also point out that boundedness results of Levin for the scalar equation $uโ(t) = - \int _0^t {a(t - s)g(u(s))ds}$ can be extended to a vector system $xโ(t) = - \int _0^t {H(t,s)x(s)ds}$.References
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- Ronald Grimmer and George Seifert, Stability properties of Volterra integrodifferential equations, J. Differential Equations 19 (1975), no.ย 1, 142โ166. MR 388002, DOI 10.1016/0022-0396(75)90025-X
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Additional Information
- © Copyright 1980 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 79 (1980), 393-399
- MSC: Primary 45J05
- DOI: https://doi.org/10.1090/S0002-9939-1980-0567979-6
- MathSciNet review: 567979