Asymptotic behavior of solutions of Volterra integro-differential equations

Mohana Rao, M. Rama; Srinivas, P.

doi:10.1090/S0002-9939-1985-0781056-5

Asymptotic behavior of solutions of Volterra integro-differential equations
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by M. Rama Mohana Rao and P. Srinivas

Proc. Amer. Math. Soc. 94 (1985), 55-60

DOI: https://doi.org/10.1090/S0002-9939-1985-0781056-5

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Abstract:

The asymptotic behavior of solutions of Volterra integrodifferential equations of the form \[ x’(t) = A(t)x(t) + \int _0^t {K(t,s)} x(s)ds + F(t)\] is discussed in which $A$ is not necessarily a stable matrix. An equivalent equation which involves an arbitrary function is derived and a proper choice of this function would pave a way for the new coefficient matrix $B$ (corresponding $A$) to be stable.

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