Search Results
You are looking at 1 - 3 of 3 items for
- Author or Editor: Tibor Krisztin x
- Refine by Access: All Content x
Periodica Mathematica Hungarica
Author:
Tibor Krisztin
Abstract
In this survey paper the delay differential equation \documentclass{aastex}
\usepackage{amsbsy}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{bm}
\usepackage{mathrsfs}
\usepackage{pifont}
\usepackage{stmaryrd}
\usepackage{textcomp}
\usepackage{upgreek}
\usepackage{portland,xspace}
\usepackage{amsmath,amsxtra}
\pagestyle{empty}
\DeclareMathSizes{10}{9}{7}{6}
\begin{document}
$$\dot x(t) = - \mu x(t) + g(x(t - 1))$$
\end{document} (t) = −µx(t) + g(x(t − 1)) is considered with µ ≥ 0 and a smooth real function g satisfying g(0) = 0. It is shown that the dynamics generated by this simple-looking equation can be very rich. The dynamics is completely
understood only for a small class of nonlinearities. Open problems are formulated.
Periodica Mathematica Hungarica
Authors:
Ábel Garab
and
Tibor Krisztin
Abstract
We consider the delay differential equation \documentclass{aastex}
\usepackage{amsbsy}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{bm}
\usepackage{mathrsfs}
\usepackage{pifont}
\usepackage{stmaryrd}
\usepackage{textcomp}
\usepackage{upgreek}
\usepackage{portland,xspace}
\usepackage{amsmath,amsxtra}
\pagestyle{empty}
\DeclareMathSizes{10}{9}{7}{6}
\begin{document}
$$\dot x(t) = - \mu x(t) + f(x(t - \tau ))$$
\end{document} , where µ, τ are positive parameters and f is a strictly monotone, nonlinear C
1-function satisfying f(0) = 0 and some convexity properties. It is well known that for prescribed oscillation frequencies (characterized by the
values of a discrete Lyapunov functional) there exists τ* > 0 such that for every τ > τ* there is a unique periodic solution. The period function is the minimal period of the unique periodic solution as a function
of τ > τ*. First we show that it is a monotone nondecreasing Lipschitz continuous function of τ with Lipschitz constant 2. As an application of our theorem we give a new proof of some recent results of Yi, Chen and Wu
[14] about uniqueness and existence of periodic solutions of a system of delay differential equations.
