Page 1 Next

Displaying 1 – 20 of 27

Showing per page

Existence and uniqueness of positive periodic solutions for a class of integral equations with parameters

Shu-Gui Kang, Bao Shi, Sui Sun Cheng (2009)

Annales Polonici Mathematici

Existence of periodic solutions of functional differential equations with parameters such as Nicholson’s blowflies model call for the investigation of integral equations with parameters defined over spaces with periodic structures. In this paper, we study one such equation ϕ ( x ) = λ [ x , x + ω ] Ω K ( x , y ) h ( y ) f ( y , ϕ ( y - τ ( y ) ) ) d y , x ∈ Ω, by means of the proper value theory of operators in Banach spaces with cones. Existence, uniqueness and continuous dependence of proper solutions are established.

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.

Positive solutions of a renewal equation

Janusz Traple (1992)

Annales Polonici Mathematici

An existence theorem is proved for the scalar convolution type integral equation x ( t ) = - h ( t - s ) f ( s , x ( s ) ) d s .

Currently displaying 1 – 20 of 27

Page 1 Next