Existence of positive solutions of linear delay difference equations with continuous time
Consider the delay difference equation with continuous time of the form \[x(t)-x(t-1)+\sum_{i=1}^mP_i(t)x(t-k_i(t))=0,\qquad t\ge t_0,\] where $P_i\colon[t_0,\infty)\mapsto\mathbb{R}$, $k_i\colon[t_0,\infty)\mapsto \{2,3,4,\dots\}$ and $\lim_{t\to\infty}(t-k_i(t))=\infty$, for $i=1,2,\dots,m$. We i...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
University of Szeged
2015-03-01
|
| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
| Subjects: | |
| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=3609 |
| Summary: | Consider the delay difference equation with continuous time of the form
\[x(t)-x(t-1)+\sum_{i=1}^mP_i(t)x(t-k_i(t))=0,\qquad t\ge t_0,\]
where $P_i\colon[t_0,\infty)\mapsto\mathbb{R}$, $k_i\colon[t_0,\infty)\mapsto \{2,3,4,\dots\}$ and $\lim_{t\to\infty}(t-k_i(t))=\infty$, for $i=1,2,\dots,m$.
We introduce the generalized characteristic equation and its importance in oscillation of all solutions of the considered difference equations. Some results for the existence of positive solutions of considered difference equations are presented as the application of the generalized characteristic equation. |
|---|---|
| ISSN: | 1417-3875 |