Stable perturbations of linear differential equations generating a uniformly bounded group

V. V. Skazka

doi:10.1070/SM8895

Stable perturbations of linear differential equations generating a uniformly bounded group

Результат исследования: Научные публикации в периодических изданиях › статья

Аннотация

Stability problems for solutions of the differential equation u′(t) = Au+ϵB(t, u) in a Banach space are considered. It is assumed that for ϵ = 0 this equation generates a uniformly bounded group of class C₀. Sufficient conditions on B and A are found under which the solutions of this equation are bounded for small ϵ. A linearization principle is proved for this equation under certain conditions on the operator B.

Язык оригинала	английский
Страницы (с-по)	1246-1259
Число страниц	14
Журнал	Sbornik Mathematics
Том	208
Номер выпуска	8
DOI	https://doi.org/10.1070/SM8895
Состояние	Опубликовано - 1 янв 2017

Доступ к документу

10.1070/SM8895

Link to publication in Scopus

Fingerprint Подробные сведения о темах исследования «Stable perturbations of linear differential equations generating a uniformly bounded group». Вместе они формируют уникальный семантический отпечаток (fingerprint).

Цитировать

@article{6c9a34cf4481442baeca4229dbc6510c,

title = "Stable perturbations of linear differential equations generating a uniformly bounded group",

abstract = "Stability problems for solutions of the differential equation u′(t) = Au+ϵB(t, u) in a Banach space are considered. It is assumed that for ϵ = 0 this equation generates a uniformly bounded group of class C0. Sufficient conditions on B and A are found under which the solutions of this equation are bounded for small ϵ. A linearization principle is proved for this equation under certain conditions on the operator B.",

keywords = "Differential equations in a Banach space, Stability of solutions, stability of solutions, differential equations in a Banach space",

author = "Skazka, {V. V.}",

year = "2017",

month = jan,

day = "1",

doi = "10.1070/SM8895",

language = "English",

volume = "208",

pages = "1246--1259",

journal = "Sbornik Mathematics",

issn = "1064-5616",

publisher = "Turpion Ltd.",

number = "8",

}

TY - JOUR

T1 - Stable perturbations of linear differential equations generating a uniformly bounded group

AU - Skazka, V. V.

PY - 2017/1/1

Y1 - 2017/1/1

N2 - Stability problems for solutions of the differential equation u′(t) = Au+ϵB(t, u) in a Banach space are considered. It is assumed that for ϵ = 0 this equation generates a uniformly bounded group of class C0. Sufficient conditions on B and A are found under which the solutions of this equation are bounded for small ϵ. A linearization principle is proved for this equation under certain conditions on the operator B.

AB - Stability problems for solutions of the differential equation u′(t) = Au+ϵB(t, u) in a Banach space are considered. It is assumed that for ϵ = 0 this equation generates a uniformly bounded group of class C0. Sufficient conditions on B and A are found under which the solutions of this equation are bounded for small ϵ. A linearization principle is proved for this equation under certain conditions on the operator B.

KW - Differential equations in a Banach space

KW - Stability of solutions

KW - stability of solutions

KW - differential equations in a Banach space

UR - http://www.scopus.com/inward/record.url?scp=85049197200&partnerID=8YFLogxK

U2 - 10.1070/SM8895

DO - 10.1070/SM8895

M3 - Article

AN - SCOPUS:85049197200

VL - 208

SP - 1246

EP - 1259

JO - Sbornik Mathematics

JF - Sbornik Mathematics

SN - 1064-5616

IS - 8

ER -