Differential and Integral Equations

Perturbing evolutionary systems by step responses and cumulative outputs

Odo Diekmann, Mats Gyllenberg, and Horst R. Thieme

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We develop a perturbation theory for strongly continuous backward evolutionary systems and their adjoint systems. The theory is not based on generating families but on certain operator families called step responses and cumulative outputs. The perturbation problem is reduced to solving an abstract Stieltjes integral equation of nonconvolution type. The theory is well suited for treating structured population models.

Article information

Differential Integral Equations, Volume 8, Number 5 (1995), 1205-1244.

First available in Project Euclid: 20 May 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 47D06: One-parameter semigroups and linear evolution equations [See also 34G10, 34K30]
Secondary: 34G10: Linear equations [See also 47D06, 47D09] 47N20: Applications to differential and integral equations 92D25: Population dynamics (general)


Diekmann, Odo; Gyllenberg, Mats; Thieme, Horst R. Perturbing evolutionary systems by step responses and cumulative outputs. Differential Integral Equations 8 (1995), no. 5, 1205--1244. https://projecteuclid.org/euclid.die/1369056052

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