This article is cited in 10 papers

The study of nonlinear almost periodic differential equations without recourse to the $\mathscr H$-classes of these equations

V. E. Slyusarchuk

Ukranian State Academy of Water Economy, Rivne

Abstract: The well-known theorems of Favard and Amerio on the existence of almost periodic solutions to linear and nonlinear almost periodic differential equations depend to a large extent on the $\mathscr H$-classes and the requirement that the bounded solutions of these equations be separated. The present paper provides different conditions for the existence of almost periodic solutions. These conditions, which do not depend on the $\mathscr H$-classes of the equations, are formulated in terms of a special functional on the set of bounded solutions of the equations under consideration. This functional is used, in particular, to test whether solutions are separated.
Bibliography: 24 titles.

Keywords: bounded and almost periodic solution, nonlinear almost periodic differential equations, Amerio's theorem.

UDC: 517.925.52

MSC: 34C27

Received: 02.11.2012 and 01.01.2014

DOI: 10.4213/sm8188

 English version: Sbornik: Mathematics, 2014, 205:6, 892–911

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