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: | , , , |
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| Format: | Article |
| Language: | English |
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University of Szeged
2015-03-01
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| 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 |
| _version_ | 1797830643270287360 |
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| author | George Chatzarakis István Győri Hajnalka Péics Ioannis Stavroulakis |
| author_facet | George Chatzarakis István Győri Hajnalka Péics Ioannis Stavroulakis |
| author_sort | George Chatzarakis |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-09T13:39:22Z |
| format | Article |
| id | doaj.art-5760792cda414de881d065ed72827719 |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:39:22Z |
| publishDate | 2015-03-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-5760792cda414de881d065ed728277192023-05-09T07:53:04ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752015-03-0120151512310.14232/ejqtde.2015.1.153609Existence of positive solutions of linear delay difference equations with continuous timeGeorge Chatzarakis0István Győri1Hajnalka Péics2Ioannis Stavroulakis3Department of Electrical and Electronic Engineering EducatorsDepartment of Mathematics and Computing, University of Pannonina, Veszprém, HungaryUniversity of Novi Sad, Subotica, Serbia and MontenegroUniversity of Ioannina, Ioannina, GreeceConsider 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.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=3609functional equationsdifference equations with continuous timepositive solutionsoscillatory solutionsnon-oscillatory solutions |
| spellingShingle | George Chatzarakis István Győri Hajnalka Péics Ioannis Stavroulakis Existence of positive solutions of linear delay difference equations with continuous time Electronic Journal of Qualitative Theory of Differential Equations functional equations difference equations with continuous time positive solutions oscillatory solutions non-oscillatory solutions |
| title | Existence of positive solutions of linear delay difference equations with continuous time |
| title_full | Existence of positive solutions of linear delay difference equations with continuous time |
| title_fullStr | Existence of positive solutions of linear delay difference equations with continuous time |
| title_full_unstemmed | Existence of positive solutions of linear delay difference equations with continuous time |
| title_short | Existence of positive solutions of linear delay difference equations with continuous time |
| title_sort | existence of positive solutions of linear delay difference equations with continuous time |
| topic | functional equations difference equations with continuous time positive solutions oscillatory solutions non-oscillatory solutions |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=3609 |
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