Bounded solutions and exponential stability for linear integro-differential equations of Volterra type

Leonid Berezansky; Alexander Domoshnitsky; Oleg Kupervasser

doi:10.1016/j.aml.2024.109112

Bounded solutions and exponential stability for linear integro-differential equations of Volterra type

Department of Mathematics

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2 Scopus citations

Abstract

For the following scalar functional–differential equation ẍ(t)+∫_t₀^tG(t,s)ẋ(s)ds+∫_t₀^tH(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.

Original language	English
Article number	109112
Journal	Applied Mathematics Letters
Volume	154
DOIs	https://doi.org/10.1016/j.aml.2024.109112
State	Published - Aug 2024

Keywords

Boundedness of all solutions
Exponential stability
Integro-differential equations of the second order
Volterra operators

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10.1016/j.aml.2024.109112

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title = "Bounded solutions and exponential stability for linear integro-differential equations of Volterra type",

abstract = "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.",

keywords = "Boundedness of all solutions, Exponential stability, Integro-differential equations of the second order, Volterra operators",

author = "Leonid Berezansky and Alexander Domoshnitsky and Oleg Kupervasser",

note = "Publisher Copyright: {\textcopyright} 2024 Elsevier Ltd",

year = "2024",

month = aug,

doi = "10.1016/j.aml.2024.109112",

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volume = "154",

journal = "Applied Mathematics Letters",

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T1 - Bounded solutions and exponential stability for linear integro-differential equations of Volterra type

AU - Berezansky, Leonid

AU - Domoshnitsky, Alexander

AU - Kupervasser, Oleg

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

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SN - 0893-9659

VL - 154

JO - Applied Mathematics Letters

JF - Applied Mathematics Letters

M1 - 109112

ER -

Bounded solutions and exponential stability for linear integro-differential equations of Volterra type

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