TY - JOUR

T1 - ON EXPONENTIAL STABILITY OF LINEAR DELAY EQUATIONS WITH OSCILLATORY COEFFICIENTS AND KERNELS

AU - Berezansky, Leonid

AU - Braverman, Elena

N1 - Funding Information:
Acknowledgment. E. Braverman was partially supported by Natural Sciences and Engineering Research Council of Canada, the grant number is RGPIN-2020-03934 in the framework of the Discovery Grant program. The authors are grateful to the anonymous referee whose thoughtful comments contributed to the current form of the paper.
Publisher Copyright:
© 2022 The authors.

PY - 2022/9/1

Y1 - 2022/9/1

N2 - New explicit exponential stability conditions are presented for the non-autonomous scalar linear functional differential equation x (t) + ∑k=1m ak(t)x(hk(t)) + ∫g(t)t K(t, s)x(s)ds = 0, where hk(t) ≤ t, g(t) ≤ t, ak(•) and the kernel K(•, •) are oscillatory and, generally, discontinuous functions. The proofs are based on establishing boundedness of solutions and later using the exponential dichotomy for linear equations stating that either the homogeneous equation is exponentially stable or a non-homogeneous equation has an unbounded solution for some bounded right-hand side. Explicit tests are applied to models of population dynamics, such as controlled Hutchinson and Mackey-Glass equations. The results are illustrated with numerical examples, and connection to known tests is discussed.

AB - New explicit exponential stability conditions are presented for the non-autonomous scalar linear functional differential equation x (t) + ∑k=1m ak(t)x(hk(t)) + ∫g(t)t K(t, s)x(s)ds = 0, where hk(t) ≤ t, g(t) ≤ t, ak(•) and the kernel K(•, •) are oscillatory and, generally, discontinuous functions. The proofs are based on establishing boundedness of solutions and later using the exponential dichotomy for linear equations stating that either the homogeneous equation is exponentially stable or a non-homogeneous equation has an unbounded solution for some bounded right-hand side. Explicit tests are applied to models of population dynamics, such as controlled Hutchinson and Mackey-Glass equations. The results are illustrated with numerical examples, and connection to known tests is discussed.

UR - http://www.scopus.com/inward/record.url?scp=85133645644&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:85133645644

SN - 0893-4983

VL - 35

SP - 559

EP - 580

JO - Differential and Integral Equations

JF - Differential and Integral Equations

IS - 9-10

ER -