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Levitan Almost Periodic Solutions of Infinite-dimensional Linear Differential Equations
Authors: David Cheban
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).
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Abstract
The known Levitan’s Theorem states that the finite-dimensional linear differential equationState University of Moldova
Faculty of Mathematics and Informatics
Department of Mathematics
A. Mateevich Street 60
MD–2009 Chisinau, Moldova
E-mail: ,
Faculty of Mathematics and Informatics
Department of Mathematics
A. Mateevich Street 60
MD–2009 Chisinau, Moldova
E-mail: ,
Fulltext
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Contents
- Limit cycles in continuous and discontinuous piecewise linear differential systems with two pieces separated by a straight line
- The problem of the center for cubic differential systems with the line at infinity and an affine real invariant straight line of total algebraic multiplicity five
- The topological classification of a family of quadratic differential systems in terms of affine invariant polynomials
- Levitan Almost Periodic Solutions of Infinite-dimensional Linear Differential Equations
- The classification of a family of cubic differential systems in terms of configurations of invariant lines of the type (3,3)
- On the upper bound of the number of functionally independent focal quantities of the Lyapunov differential system
- On limit cycles of polynomial systems of the first-order ODEs
- Sufficient GL(2,R)-invariant center conditions for some classes of two-dimensional cubic differential systems.
- Invariant conditions of stability of unperturbed motion governed by critical differential systems s(1,2,3)
- Working with professor Nicolae Vulpe
