Unified approach to bounded, periodic and almost periodic solutions of differential systems
Abstract
The criteria for an entirely bounded solution of a quasi-linear differential system are developed via asymptotic boundary value problems. The same principle allows us to deduce at the same time the existence of periodic orbits, when assuming additionally periodicity in time variables of the related right-hand sides. For almost periodicity, the situation is unfortunately not so straightforward. Nevertheless, for the Lipschitzean uniformly almost periodic (in time variables) systems, we are able to show that every bounded solution becomes almost periodic as well.
Keywords
asymptotic boundary value problems; boundedness; periodicity; almost periodicity; unified approach
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Department of Mathematical Analysis, Faculty of Science, Palacký Univeristy, Czech Republic Czechia
Department of Mathematical Analysis, Faculty of Electrical Engineering and Informatics, Technical Univeristy of Ostrava, Czech Republic Czechia
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