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 -