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

نتاج البحث: نشر في مجلة › مقالة › مراجعة النظراء

2 اقتباسات (Scopus)

ملخص

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.

اللغة الأصلية	الإنجليزيّة
رقم المقال	109112
دورية	Applied Mathematics Letters
مستوى الصوت	154
المعرِّفات الرقمية للأشياء	https://doi.org/10.1016/j.aml.2024.109112
حالة النشر	نُشِر - أغسطس 2024

الوصول إلى المستند

10.1016/j.aml.2024.109112

الملفات والروابط الأخرى

Link to publication in Scopus

قم بذكر هذا

@article{b59c13fd29d649cfb413d99496dd5918,

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",

language = "אנגלית",

volume = "154",

journal = "Applied Mathematics Letters",

issn = "0893-9659",

publisher = "Elsevier Ltd.",

}

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

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 - https://www.scopus.com/pages/publications/85190735034

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 -

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

ملخص

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الملفات والروابط الأخرى

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