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

Y1 - 2024/8

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 - 10.1016/j.aml.2024.109112

DO - 10.1016/j.aml.2024.109112

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AN - SCOPUS:85190735034

SN - 0893-9659

VL - 154

JO - Applied Mathematics Letters

JF - Applied Mathematics Letters

M1 - 109112

ER -