Wiman’s formula for a second order dynamic equation

Authors

Lynn Erbe, University of Nebraska-LincolnFollow
Gro Hovhannisyan, Kent State University - Stark CampusFollow
Allan C. Peterson, University of Nebraska-LincolnFollow

Date of this Version

2014

Citation

Advances in Difference Equations 2014, 2014:61

Comments

©2014 Erbe et al.

This is an open access article

Abstract

We derive Wiman’s asymptotic formula for the number of generalized zeros of (nontrivial) solutions of a second order dynamic equation on a time scale. The proof is based on the asymptotic representation of solutions via exponential functions on a time scale. By using the Jeffreys et al. approximation we prove Wiman’s formula for a dynamic equation on a time scale. Further we show that using the Hartman-Wintner approximation one can derive another version of Wiman’s formula. We also prove some new oscillation theorems and discuss the results by means of several examples.