Stability Properties of Linear Volterra Integrodifferential Equations in a Banach Space

MR2197535 Hino, Yoshiyuki and Murakami, Satoru Yoshiyuki HINO and Satoru MURAKAMI Stability Properties of Linear Volterra Integrodifferential Equations in a Banach Space Funkcialaj Ekvacioj. Serio Internacia 48 2005 367--392 http://fe.math.kobe-u.ac.jp/FE/FullPapers/48-3/48_367.pdf http://www.ams.org/mathscinet-getitem?mr=MR2197535 For linear Volterra integrodifferential 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. Volterra integrodifferential equation, Stabilities, Resolvent operator, Asymptotically almost periodic solutions. Primary 34K14; Secondary 34K30. 48-367 2005 Stability Properties of Linear Volterra Integrodifferential Equations in a Banach Space HINO, Yoshiyuki and MURAKAMI, Satoru Yoshiyuki HINO and Satoru MURAKAMI

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