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Bul. Acad. Ştiinţe Repub. Mold. Mat., 2019, номер 2, страницы 56–78
(Mi basm510)
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Levitan almost periodic solutions of infinite-dimensional linear differential equations
David Cheban State University of Moldova,
Faculty of Mathematics and Informatics,
Department of Mathematics,
A. Mateevich Street 60,
MD–2009 Chişinău, Moldova
Аннотация:
The known Levitan's Theorem states that the finite-dimensional linear differential equation
\begin{equation} x'=A(t)x+f(t) \end{equation}
with Bohr almost periodic coefficients $A(t)$ and $f(t)$ admits at least one Levitan almost periodic solution if it has a bounded solution. The main assumption in this theorem is the separation among bounded solutions of homogeneous equations
\begin{equation} x'=A(t)x. \end{equation}
In this paper we prove that infinite-dimensional linear differential equation (1) with Levitan almost periodic coefficients has a Levitan almost periodic solution if it has at least one relatively compact solution and the trivial solution of equation (2) is Lyapunov stable. We study the problem of existence of Bohr/Levitan almost periodic solutions for infinite-dimensional equation (1) in the framework of general nonautonomous dynamical systems (cocycles).
Ключевые слова и фразы:
Levitan almost periodic solution, linear differential equation, common fixed point for noncommutative affine semigroups of affine mappings.
Полный текст:
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Список литературы:
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Тип публикации:
Статья
MSC: 34C27, 34G10, 35B15 Поступила в редакцию: 08.08.2019
Язык публикации: английский
Образец цитирования:
David Cheban, “Levitan almost periodic solutions of infinite-dimensional linear differential equations”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2019, no. 2, 56–78
Цитирование в формате AMSBIB
\RBibitem{Che19}
\by David~Cheban
\paper Levitan almost periodic solutions of infinite-dimensional linear differential equations
\jour Bul. Acad. \c Stiin\c te Repub. Mold. Mat.
\yr 2019
\issue 2
\pages 56--78
\mathnet{http://mi.mathnet.ru/basm510}
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