๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

On the second-order differential equation with piecewise constant argument and almost periodic coefficients

โœ Scribed by Rong Yuan

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
233 KB
Volume
52
Category
Article
ISSN
0362-546X

No coin nor oath required. For personal study only.

โœฆ Synopsis

In this paper, we study the existence of almost and quasi-periodic solutions to two classes of second-order di erential equations. As a corollary, it is shown that periodic and unbounded solutions can coexist for the equation x (t) + ! 2 x(t) = bx([t]) + f(t), which is di erent from the case: b = 0. This phenomena is due to the piecewise constant argument and illustrates a crucial di erence between ordinary di erential equations and di erential equations with piecewise constant argument. The results are extended to nonlinear equations.

๐Ÿ“œ SIMILAR VOLUMES

Almost periodic solutions of second-orde
Almost periodic solutions of second-order neutral equations with piecewise constant arguments
โœ Hong-Xu Li ๐Ÿ“‚ Article ๐Ÿ“… 2006 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 186 KB

In this paper, we present a theorem on the almost periodic solutions of second-order neutral equations with piecewise constant arguments of the form where [โ€ข] denotes the greatest integer function, p, q (| p| > 1 or p = -1) are nonzero constants, and f (t) is almost periodic.