TY - JOUR
T1 - Bounded solutions and exponential stability for linear integro-differential equations of Volterra type
AU - Berezansky, Leonid
AU - Domoshnitsky, Alexander
AU - Kupervasser, Oleg
N1 - Publisher Copyright: © 2024 Elsevier Ltd
PY - 2024/8/1
Y1 - 2024/8/1
N2 - For the following scalar functional–differential equation ẍ(t)+∫t0tG(t,s)ẋ(s)ds+∫t0tH(t,s)x(s)ds=f(t),t≥t0,we obtain sufficient conditions for boundedness of all solutions and uniform exponential stability for the homogeneous equation. As examples, equations with singular kernels and equations with bounded delays ẍ(t)+∫g(t)tG(t,s)ẋ(s)ds+∫h(t)tH(t,s)x(s)ds=f(t),t≥t0,are considered.
AB - For the following scalar functional–differential equation ẍ(t)+∫t0tG(t,s)ẋ(s)ds+∫t0tH(t,s)x(s)ds=f(t),t≥t0,we obtain sufficient conditions for boundedness of all solutions and uniform exponential stability for the homogeneous equation. As examples, equations with singular kernels and equations with bounded delays ẍ(t)+∫g(t)tG(t,s)ẋ(s)ds+∫h(t)tH(t,s)x(s)ds=f(t),t≥t0,are considered.
KW - Boundedness of all solutions
KW - Exponential stability
KW - Integro-differential equations of the second order
KW - Volterra operators
UR - http://www.scopus.com/inward/record.url?scp=85190735034&partnerID=8YFLogxK
U2 - https://doi.org/10.1016/j.aml.2024.109112
DO - https://doi.org/10.1016/j.aml.2024.109112
M3 - Article
SN - 0893-9659
VL - 154
JO - Applied Mathematics Letters
JF - Applied Mathematics Letters
M1 - 109112
ER -