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On monotonic solutions of some integral equations

J. Caballero, Donal O'Regan, K. B. Sadarangani (2005)

Archivum Mathematicum

The aim of this paper is to obtain monotonic solutions of an integral equation of Urysohn-Stieltjes type in C [ 0 , 1 ] . Existence will be established with the aid of the measure of noncompactness.

On stability and robust stability of positive linear Volterra equations in Banach lattices

Satoru Murakami, Pham Ngoc (2010)

Open Mathematics

We study positive linear Volterra integro-differential equations in Banach lattices. A characterization of positive equations is given. Furthermore, an explicit spectral criterion for uniformly asymptotic stability of positive equations is presented. Finally, we deal with problems of robust stability of positive systems under structured perturbations. Some explicit stability bounds with respect to these perturbations are given.

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