A Test for Global Attractivity of Linear Dynamic Equations with Delay

Abstract

In this paper, we consider the delay dynamic equation Based on Lyapunov’s method, we study global attractivity of the trivial solution of (∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$*$$\\end{document}). Our new result generalizes some well-known results in the theory of difference and differential equations to dynamic equations of the form (∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$*$$\\end{document}). We also present some examples on nonstandard time scales to illustrate the importance of the new result.