Necessary and sufficient conditions for existence and uniqueness of bounded or almost-periodic solutions for differential systems with convex potential. (English) Zbl 1212.34112

Cieutat, Philippe

Differ. Integral Equ. 18, No. 4, 361-378 (2005).

The system \(u'+\nabla \Phi (u)=e(t)\) with \(u\:\mathbb R\to \mathbb R^N\), \(\Phi \:\mathbb R^N\to \mathbb R\) (\(\Phi \) convex), and \(e\:\mathbb R\to \mathbb R^N\) is considered. Necessary and sufficient conditions for the existence and uniqueness of bounded or almost-periodic solutions are given.

Reviewer: Ivan Straškraba (Praha)

MSC:

34C11	Growth and boundedness of solutions to ordinary differential equations
34C27	Almost and pseudo-almost periodic solutions to ordinary differential equations

Keywords:

first-order differential system; bounded or almost-periodic solutions