Existence of positive solutions in a delay logistic difference equation

Abstract

The author studied the existence of positive solutions of the delay logistic difference equation

\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\Delta \gamma _n = p_n \gamma _n (1 - \gamma _{\tau (n)} ),n = 0,1,2,....$$\end{document}

where {p_n} is a sequence of positive real numbers, {τ(n)} is a nondecreasing sequence of integers, τ(n)<n and \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\mathop {\lim }\limits_{n \to \infty } $$\end{document} τ (n)=∞. A sufficient condition for the existence of positive solutions of the equation was given.

Keywords

positive solutions / logistic delay difference equation / oscillation

References

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