# Masaryk University

Publication details

# How the constants in Hille-Nehari theorems depend on time scales

Authors 2006 Article in Periodical Advances in Difference Equations General mathematics Hille-Nehari criteria; oscillation criteria; time scales; dynamic equation on time scales We present criteria of Hille--Nehari type for the linear dynamic equation $(r(t)y\del)\del+p(t)y\sig=0$, i.e., the criteria in terms of the limit behavior of $\left(\int_a^t 1/r(s)\,\dd s\right)\int_t^\infty p(s)\,\dd s$ as $t\to\infty$. As a particular important case, we get that there is a (sharp) critical constant in those criteria which belongs to the interval $[0,1/4]$, and its value depends on the graininess $\mu$ and the coefficient $r$. Also we offer some applications, e.g., criteria for strong (non)oscillation and Kneser type criteria, comparison with existing results (our theorems turn out to be new even in the discrete case as well as in many other situations), and comments with examples.