Publication details

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

Investor logo


Year of publication 2006
Type Article in Periodical
Magazine / Source Advances in Difference Equations
MU Faculty or unit

Faculty of Education

Field General mathematics
Keywords Hille-Nehari criteria; oscillation criteria; time scales; dynamic equation on time scales
Description 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.
Related projects:

You are running an old browser version. We recommend updating your browser to its latest version.

More info