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Sbornik: Mathematics, 2017, Volume 208, Issue 8, Pages 1246–1259
DOI: https://doi.org/10.1070/SM8895 (Mi sm8895) 		 
Stable perturbations of linear differential equations generating a uniformly bounded group

V. V. Skazkaab

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
b Novosibirsk State University
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DOI: https://doi.org/10.1070/SM8895
Abstract: Stability problems for solutions of the differential equation $u'(t)=Au+\varepsilon B(t,u)$ in a Banach space are considered. It is assumed that for $\varepsilon=0$ this equation generates a uniformly bounded group of class $C_0$. Sufficient conditions on $B$ and $A$ are found under which the solutions of this equation are bounded for small $\varepsilon$. A linearization principle is proved for this equation under certain conditions on the operator $B$.
Bibliography: 9 titles.
Keywords: differential equations in a Banach space, stability of solutions.
Received: 27.12.2016
Russian version:
Matematicheskii Sbornik, 2017, Volume 208, Number 8, Pages 168–182
DOI: https://doi.org/10.4213/sm8895
Bibliographic databases:
Document Type: Article
UDC: 517.95
MSC: Primary 34G10; Secondary 34D05, 70K28
Language: English
Original paper language: Russian
Citation: V. V. Skazka, “Stable perturbations of linear differential equations generating a uniformly bounded group”, Mat. Sb., 208:8 (2017), 168–182; Sb. Math., 208:8 (2017), 1246–1259
Citation in format AMSBIB
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    References:53
    First page:25
     
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