I. U. Bronshtein's conjecture for monotone nonautonomous dynamical systems

David Cheban

doi:10.3934/dcdsb.2019008

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2019, Volume 24, Issue 3: 1095-1113. Doi: 10.3934/dcdsb.2019008

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I. U. Bronshtein's conjecture for monotone nonautonomous dynamical systems

David Cheban^,

State University of Moldova, Faculty of Mathematics and Informatics, Department of Mathematics, A. Mateevich Street 60, Chișinău, MD 2009, Moldova

^* Corresponding author: David Cheban
^* Corresponding author: David Cheban

Received: November 2017

Revised: January 2018

Early access: January 2019

Published: January 2019

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Abstract

In this paper we study the problem of Levitan/Bohr almost periodicity of solutions for dissipative differential equations (Bronshtein's conjecture for Bohr almost periodic case). We give a positive answer to this conjecture for monotone Levitan/Bohr almost periodic systems of differential/difference equations.

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Mathematics Subject Classification: Primary: 34C12, 34C27, 34D20, 37B20, 37B55.

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