Equations with infinite delay: blending the abstract and the concrete

O. Diekmann; M. Gyllenberg

doi:10.1016/j.jde.2011.09.038

Equations with infinite delay: blending the abstract and the concrete

O. Diekmann, M. Gyllenberg^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › Academic › peer-review

Abstract

Using perturbation theory for adjoint semigroups (a modification of sun-star calculus) we prove, in the case of infinite delay, the principle of linearized stability for nonlinear renewal equations, delay-differential equations and coupled systems of these two types of equations. Our results extend those of Diekmann et al. (1995) [13] and Diekmann et al. (2007) [14] to the case of infinite delay.

Original language	English
Pages (from-to)	819-851
Number of pages	33
Journal	Journal of Differential Equations
Volume	252
Issue number	2
DOIs	https://doi.org/10.1016/j.jde.2011.09.038
Publication status	Published - 15 Jan 2012

Keywords

Wiskunde en Informatica (WIIN)
Mathematics
Wiskunde en computerwetenschappen
Landbouwwetenschappen
Wiskunde: algemeen

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10.1016/j.jde.2011.09.038

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title = "Equations with infinite delay: blending the abstract and the concrete",

abstract = "Using perturbation theory for adjoint semigroups (a modification of sun-star calculus) we prove, in the case of infinite delay, the principle of linearized stability for nonlinear renewal equations, delay-differential equations and coupled systems of these two types of equations. Our results extend those of Diekmann et al. (1995) [13] and Diekmann et al. (2007) [14] to the case of infinite delay.",

keywords = "Wiskunde en Informatica (WIIN), Mathematics, Wiskunde en computerwetenschappen, Landbouwwetenschappen, Wiskunde: algemeen",

author = "O. Diekmann and M. Gyllenberg",

year = "2012",

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AU - Diekmann, O.

AU - Gyllenberg, M.

PY - 2012/1/15

Y1 - 2012/1/15

N2 - Using perturbation theory for adjoint semigroups (a modification of sun-star calculus) we prove, in the case of infinite delay, the principle of linearized stability for nonlinear renewal equations, delay-differential equations and coupled systems of these two types of equations. Our results extend those of Diekmann et al. (1995) [13] and Diekmann et al. (2007) [14] to the case of infinite delay.

AB - Using perturbation theory for adjoint semigroups (a modification of sun-star calculus) we prove, in the case of infinite delay, the principle of linearized stability for nonlinear renewal equations, delay-differential equations and coupled systems of these two types of equations. Our results extend those of Diekmann et al. (1995) [13] and Diekmann et al. (2007) [14] to the case of infinite delay.

KW - Wiskunde en Informatica (WIIN)

KW - Mathematics

KW - Wiskunde en computerwetenschappen

KW - Landbouwwetenschappen

KW - Wiskunde: algemeen

U2 - 10.1016/j.jde.2011.09.038

DO - 10.1016/j.jde.2011.09.038

M3 - Article

SN - 0022-0396

VL - 252

SP - 819

EP - 851

JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 2

ER -

Equations with infinite delay: blending the abstract and the concrete

Abstract

Keywords

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