Characterizations of linear Volterra integral equations with nonnegative kernels

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:335

Article

Naito, Toshiki ; Shin, Jong Son ; Murakami, Satoru ; Ngoc, Pham Huu Anh

关键词: linear Volterra integral equation;    positive system;    Paley-Wiener theorem;    Perron-Frobenius theorem;    C-0-semigroup;   

DOI  :  10.1016/j.jmaa.2007.01.070

来源: Elsevier

【 摘 要 】

We first introduce the notion of positive linear Volterra integral equations. Then, we offer a criterion for positive equations in terms of the resolvent. In particular, equations with nonnegative kernels are positive. Next, we obtain a variant of the Paley-Wiener theorem for equations of this class and its extension to perturbed equations. Furthermore, we get a Perron-Frobenius type theorem for linear Volterra integral equations with nonnegative kernels. Finally, we give a criterion for positivity of the initial function semigroup of linear Volterra integral equations and provide a necessary and sufficient condition for exponential stability of the semigroups. (C) 2007 Elsevier Inc. All rights reserved.

【 授权许可】

Free