## Differential and Integral Equations

### Almost-periodic and bounded solutions of Carathéodory differential inclusions

Jan Andres

#### Abstract

The main purpose of this paper is two-fold: to find sufficient conditions for the existence of entirely bounded solutions of Carathéodory quasi-linear differential inclusions and to show that, if the coefficients are specially constant and the right-hand sides are additionally Lipschitz continuous (with a sufficiently small Lipschitz constant) and almost-periodic in time, then these solutions become almost-periodic as well. The almost-periodicity is understood in the sense of H. Weyl and, because of set-valued analysis, we introduce for the first time the appropriately generalized concept. The related methods, including the fixed-point theorem for a class of $\mathcal{J}$-maps in locally convex topological vector spaces, are developed here too. In the single-valued case, the obtained criteria generalize those of the other authors.

#### Article information

Source
Differential Integral Equations, Volume 12, Number 6 (1999), 887-912.

Dates
First available in Project Euclid: 29 April 2013

Permanent link to this document
https://projecteuclid.org/euclid.die/1367241480

Mathematical Reviews number (MathSciNet)
MR1728035

Zentralblatt MATH identifier
1017.34011

#### Citation

Andres, Jan. Almost-periodic and bounded solutions of Carathéodory differential inclusions. Differential Integral Equations 12 (1999), no. 6, 887--912. https://projecteuclid.org/euclid.die/1367241480