Bounded Particular Solution of a Non-homogeneous System of Two Discrete Equations

conference paper

English

In the paper we consider a two-dimensional linear non-homogeneous system of discrete equations y(1)(k + 1) = ay(1)(k) + py(2)(k) + g(1)(k), y(2)(k + 1) = -qy(1)(k) + ay(2)(k) + g(2)(k), where k = k(0), k(0) + 1, ... with k(0) a fixed integer, a, p > 0, q > 0 are real constants and g(i): {k(0), k(0) + 1, ...}. R, i = 1, 2 are given functions. Sufficient conditions are derived guaranteeing the existence of a solution y(k) = (y(1)(k), y(2)(k))(T), k = k(0), k(0) + 1, ... satisfying alpha y(1)(2)(k) + beta y(2)(2)(k) < M, where M, alpha and beta are positive fixed constants such that alpha p = beta q.

discrete system; bounded solution; linear planar system

BAŠTINEC, J.; DIBLÍK, J.

7. 6. 2024

American Institute of Physics

USA

9780735449541

AIP Conference Proceedings, Volume 3094, Issue 1, 7 June 2024, International Conference of Numerical Analysis and Applied Mathematics 2022, ICNAAM 2022

0094-243X

AIP conference proceedings

3094

1

United States of America

400001-1

400001-4

4

https://pubs.aip.org/aip/acp/article/3094/1/400001/3297294/Bounded-particular-solution-of-a-non-homogeneous