EUDML

Currently displaying 1 – 4 of 4

Order by Relevance | Title | Year of publication

Existence and global attractivity of periodic solutions in a higher order difference equation

Chuanxi Qian; Justin Smith — 2018

Archivum Mathematicum

Consider the following higher order difference equation $x (n + 1) = f (n, x (n)) + g (n, x (n - k)), n = 0, 1, \dots$ where $f (n, x)$ and $g (n, x) : {0, 1, \dots} \times [0, \infty) \to [0, \infty)$ are continuous functions in $x$ and periodic functions in $n$ with period $p$ , and $k$ is a nonnegative integer. We show the existence of a periodic solution ${\tilde{x} (n)}$ under certain conditions, and then establish a sufficient condition for ${\tilde{x} (n)}$ to be a global attractor of all nonnegative solutions of the equation. Applications to Riccati difference equation and some other difference equations derived from mathematical biology are also given.

Page 1

Download Results (CSV)

Advanced Search

Formula preview

Currently displaying 1 – 4 of 4

Existence and global attractivity of periodic solutions in a higher order difference equation

On asymptotic behaviour of oscillatory solutions for fourth order differential equations.

Global attractivity in a nonlinear difference equation.

Multiple positive solutions of a boundary value problem for ordinary differential equations.