TY - JOUR

T1 - Solution estimates and stability tests for linear neutral differential equations

AU - Berezansky, Leonid

AU - Braverman, Elena

N1 - Funding Information:
The second author acknowledges the support of NSERC, Canada , the grant RGPIN-2020-03934 .
Publisher Copyright:
© 2020 Elsevier Ltd

PY - 2020/10/1

Y1 - 2020/10/1

N2 - Explicit exponential stability tests are obtained for the scalar neutral differential equation ẋ(t)−a(t)ẋ(g(t))=−∑k=1mbk(t)x(hk(t)), together with exponential estimates for its solutions. Estimates for solutions of a non-homogeneous neutral equation are also obtained, they are valid on every finite segment, thus describing both asymptotic and transient behavior. For neutral differential equations, exponential estimates are obtained here for the first time. Both the coefficients and the delays are assumed to be measurable, not necessarily continuous functions.

AB - Explicit exponential stability tests are obtained for the scalar neutral differential equation ẋ(t)−a(t)ẋ(g(t))=−∑k=1mbk(t)x(hk(t)), together with exponential estimates for its solutions. Estimates for solutions of a non-homogeneous neutral equation are also obtained, they are valid on every finite segment, thus describing both asymptotic and transient behavior. For neutral differential equations, exponential estimates are obtained here for the first time. Both the coefficients and the delays are assumed to be measurable, not necessarily continuous functions.

KW - Explicit solution estimates

KW - Exponential stability tests

KW - Linear neutral differential equations

KW - Variable delays and coefficients

UR - http://www.scopus.com/inward/record.url?scp=85085729762&partnerID=8YFLogxK

U2 - 10.1016/j.aml.2020.106515

DO - 10.1016/j.aml.2020.106515

M3 - Article

AN - SCOPUS:85085729762

VL - 108

JO - Applied Mathematics Letters

JF - Applied Mathematics Letters

SN - 0893-9659

M1 - 106515

ER -