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Differential equations. Integral equations. Other functional equations. Finite differences. Calculus of variations. Functional analysis (173) 
Computational mathematics. Numerical analysis (108) 
SM ISO690:2012 CHEBAN, David. Levitan Almost Periodic Solutions of Infinitedimensional Linear Differential Equations. In: Buletinul Academiei de Ştiinţe a Moldovei. Matematica. 2019, nr. 2(90), pp. 5678. ISSN 10247696. 
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Buletinul Academiei de Ştiinţe a Moldovei. Matematica  
Numărul 2(90) / 2019 / ISSN 10247696  


CZU: 517.926+519.6  
MSC 2010: 34C27, 34G10, 35B15.  
Pag. 5678 



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The known Levitan’s Theorem states that the finitedimensional 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 infinitedimensional 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 infinitedimensional equation (3) in the framework of general nonautonomous dynamical systems (cocycles). 

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


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<?xml version='1.0' encoding='utf8'?> <oai_dc:dc xmlns:dc='http://purl.org/dc/elements/1.1/' xmlns:oai_dc='http://www.openarchives.org/OAI/2.0/oai_dc/' xmlns:xsi='http://www.w3.org/2001/XMLSchemainstance' xsi:schemaLocation='http://www.openarchives.org/OAI/2.0/oai_dc/ http://www.openarchives.org/OAI/2.0/oai_dc.xsd'> <dc:creator>Ceban, D.</dc:creator> <dc:date>20191227</dc:date> <dc:description xml:lang='en'><p>The known Levitan’s Theorem states that the finitedimensional 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 infinitedimensional 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 infinitedimensional equation (3) in the framework of general nonautonomous dynamical systems (cocycles).</p></dc:description> <dc:source>Buletinul Academiei de Ştiinţe a Moldovei. Matematica 90 (2) 5678</dc:source> <dc:subject>Levitan almost periodic solution linear differential equation common fixed point for noncommutative affine semigroups of affine mappings</dc:subject> <dc:title><p>Levitan Almost Periodic Solutions of Infinitedimensional Linear Differential Equations</p></dc:title> <dc:type>info:eurepo/semantics/article</dc:type> </oai_dc:dc>