Stability Properties of Linear Volterra Integrodifferential Equations in a Banach Space
Stability Properties of Linear Volterra Integrodifferential Equations in a Banach Space
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DOI：
10.1619/fesi.48.367
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发表时间：
2005
期刊：
影响因子：
--
通讯作者：
Y. Hino;S. Murakami
中科院分区：
文献类型：
--
作者：
Y. Hino;S. Murakami
。对于线性Volterra积分方程解的一致渐近稳定性，我们用预解算子的一个性质刻画了零解的一致渐近稳定性。特别地，对于卷积型方程，我们利用预解算子的可积性和特征算子的可逆性刻画了一致渐近稳定性。此外，我们将我们的结果应用于具有渐近概周期项的非齐次方程，并建立了关于渐近概周期解存在性的一些结果。
. For linear Volterra integrodi¤erential equations, we characterize the uniform asymptotic stability property of the zero solution by a property for the resolvent operator. In particular, for equations of convolution type, we characterize the uniform asymptotic stability property in terms of the integrability of the resolvent operator, as well as the invertibility of the characteristic operator. Furthermore, we apply our results to nonhomogeneous equations with asymptotically almost periodic forcing terms, and establish some results on the existence of asymptotically almost periodic solutions.