### Abstract

Consider the delay difference equation with continuous time of the form where P_{i}: [t_{0}, ¥) ® R, k_{i}: [t_{0}, ¥) ® {2, 3, 4,...} and lim_{t}_{®}_{¥} (t - k_{i}(t)) = ¥, for i = 1, 2,...,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.

Original language | English |
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Article number | A15 |

Journal | Electronic Journal of Qualitative Theory of Differential Equations |

Volume | 2015 |

Publication status | Published - Jan 1 2015 |

### Keywords

- Difference equations with continuous time
- Functional equations
- Non-oscillatory solutions
- Oscillatory solutions
- Positive solutions

### ASJC Scopus subject areas

- Applied Mathematics

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## Cite this

Chatzarakis, G. E., Győri, I., Péics, H., & Stavroulakis, I. P. (2015). Existence of positive solutions of linear delay difference equations with continuous time.

*Electronic Journal of Qualitative Theory of Differential Equations*,*2015*, [A15].