文章基本信息

标题：Wiman’s formula for a second order dynamic equation
本地全文：下载
作者：Lynn Erbe ; Gro Hovhannisyan ; Alan Peterson 等
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2014
卷号：2014
期号：1
页码：61
DOI：10.1186/1687-1847-2014-61
语种：English
出版社：Hindawi Publishing Corporation
摘要：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. MSC:34E20, 34N05.
关键词：dynamic equation on a time scale ; oscillation theory ; number of zeros ; asymptotic representation of solutions ; Jeffreys, Wentzel, Kramers and Brillouin approximation