Levitan/Bohr almost periodic and almost automorphic solutions of scalar differential equations
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CHEBAN, David. Levitan/Bohr almost periodic and almost automorphic solutions of scalar differential equations. In: Dynamical Systems, 2018, nr. 4(33), pp. 667-690. ISSN 1468-9367. DOI: https://doi.org/10.1080/14689367.2018.1433817
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Dynamical Systems
Numărul 4(33) / 2018 / ISSN 1468-9367

Levitan/Bohr almost periodic and almost automorphic solutions of scalar differential equations

DOI: https://doi.org/10.1080/14689367.2018.1433817

Pag. 667-690

Cheban David
 
Moldova State University
 
Disponibil în IBN: 4 decembrie 2018


Rezumat

The aim of this paper is to prove the existence of Levitan/Bohr almost periodic, almost automorphic, recurrent and Poisson stable solutions of the scalar differential equations. The existence of at least one quasi-periodic (respectively, Bohr almost periodic, almost automorphic, recurrent, pseudo recurrent, Levitan almost periodic, almost recurrent, Poisson stable) solution of sclalar differential equations is proved under the condition that it admits at least one bounded solution on the positive semi-axis which is uniformly Lyapunov stable.

Cuvinte-cheie
almost automorphic solutions,

Bohr/Levitan almost periodic solution, cocycle,

non-autonomous dynamical systems, scalar differential equations, uniform stability