Characterizations of linear Volterra integral equations with nonnegative kernels

[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.

[发布日期] 2007-11-01

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