Levitan Almost Periodic Solutions of Infinite-dimensional Linear Differential Equations
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Differential equations. Integral equations. Other functional equations. Finite differences. Calculus of variations. Functional analysis (172)
Computational mathematics. Numerical analysis (102)
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CHEBAN, David. Levitan Almost Periodic Solutions of Infinite-dimensional Linear Differential Equations. In: Buletinul Academiei de Ştiinţe a Moldovei. Matematica. 2019, nr. 2(90), pp. 56-78. ISSN 1024-7696.
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Buletinul Academiei de Ştiinţe a Moldovei. Matematica
Numărul 2(90) / 2019 / ISSN 1024-7696

Levitan Almost Periodic Solutions of Infinite-dimensional Linear Differential Equations

CZU: 517.926+519.6
MSC 2010: 34C27, 34G10, 35B15.

Pag. 56-78

Cheban David
 
State University of Moldova
 
Disponibil în IBN: 3 ianuarie 2020


Rezumat

The known Levitan’s Theorem states that the finite-dimensional linear differential equation x′ = A(t)x + f(t) (1) 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 x′ = A(t)x . (2) In this paper we prove that infinite-dimensional linear differential equation (3) 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 (3) in the framework of general nonautonomous dynamical systems (cocycles).

Cuvinte-cheie
Levitan almost periodic solution linear differential equation common fixed point for noncommutative affine semigroups of affine mappings

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