The limits of solutions of a linear delay integral equation

Kazuki Himoto; Hideaki Matsunaga

doi:10.3934/dcdsb.2020050

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2020, Volume 25, Issue 8: 3033-3048. Doi: 10.3934/dcdsb.2020050

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The limits of solutions of a linear delay integral equation

Kazuki Himoto and
Hideaki Matsunaga^,

Department of Mathematical Sciences, Osaka Prefecture University, Sakai 599-8531, Japan

^* Corresponding author: Hideaki Matsunaga
^* Corresponding author: Hideaki Matsunaga

Received: March 2019

Revised: October 2019

Early access: February 2020

Published: August 2020

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Abstract

In this paper we classify the limits of solutions of a linear integral equation with finite delay. In particular, if the solution tends to a point or a periodic orbit, we establish the explicit expressions depending on given initial functions by using analysis of characteristic roots and the formal adjoint theory. Our results also present a necessary and sufficient condition for the exponential stability of the equation.

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Mathematics Subject Classification: Primary: 45A05, 45F05; Secondary: 34K25.

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References

[1]	T. Alarcón, P. Getto and Y. Nakata, Stability analysis of a renewal equation for cell population dynamics with quiescence, SIAM J. Appl. Math., 74 (2014), 1266-1297. doi: 10.1137/130940438.
[2]	T. A. Burton, Volterra Integral and Differential Equations, Mathematics in Science and Engineering, 202, Elsevier B. V., Amsterdam, 2005.
[3]	C. Corduneanu, Integral Equations and Applications, Cambridge University Press, Cambridge, 1991. doi: 10.1017/CBO9780511569395.
[4]	O. Diekmann and M. Gyllenberg, Equations with infinite delay: Blending the abstract and the concrete, J. Differential Equations, 252 (2012), 819-851. doi: 10.1016/j.jde.2011.09.038.
[5]	G. Gripenberg, S.-O. Londen and O. Staffans, Volterra Integral and Functional Equations, Encyclopedia of Mathematics and its Applications, 34, Cambridge University Press, Cambridge, 1990. doi: 10.1017/CBO9780511662805.
[6]	H. Inaba, Age-Structured Population Dynamics in Demography and Epidemiology, Springer, Singapore, 2017. doi: 10.1007/978-981-10-0188-8.
[7]	H. Matsunaga, S. Murakami and V. M. Nguyen, Decomposition and variation-of-constants formula in the phase space for integral equations, Funkcial. Ekvac., 55 (2012), 479-520. doi: 10.1619/fesi.55.479.
[8]	H. Matsunaga, S. Murakami and Y. Nagabuchi, Formal adjoint operators and asymptotic formula for solutions of autonomous linear integral equations, J. Math. Anal. Appl., 410 (2014), 807-826. doi: 10.1016/j.jmaa.2013.08.035.
[9]	D. Melchor-Aguilar, On stability of integral delay systems, Appl. Math. Comput., 217 (2010), 3578-3584. doi: 10.1016/j.amc.2010.08.058.