Open Access
Translator Disclaimer
29 June 2004 On certain comparison theorems for half-linear dynamic equations on time scales
Pavel Řehák
Abstr. Appl. Anal. 2004(7): 551-565 (29 June 2004). DOI: 10.1155/S1085337504306251

Abstract

We obtain comparison theorems for the second-order half-linear dynamic equation [r(t)Φ(yΔ)]Δ+p(t)Φ(yσ)=0, where Φ(x)=|x|α1sgnx with α>1. In particular, it is shown that the nonoscillation of the previous dynamic equation is preserved if we multiply the coefficient p(t) by a suitable function q(t) and lower the exponent α in the nonlinearity Φ, under certain assumptions. Moreover, we give a generalization of Hille-Wintner comparison theorem. In addition to the aspect of unification and extension, our theorems provide some new results even in the continuous and the discrete case.

Citation

Download Citation

Pavel Řehák. "On certain comparison theorems for half-linear dynamic equations on time scales." Abstr. Appl. Anal. 2004 (7) 551 - 565, 29 June 2004. https://doi.org/10.1155/S1085337504306251

Information

Published: 29 June 2004
First available in Project Euclid: 7 July 2004

zbMATH: 1068.34031
MathSciNet: MR2084935
Digital Object Identifier: 10.1155/S1085337504306251

Subjects:
Primary: 34C10 , 39A10

Rights: Copyright © 2004 Hindawi

JOURNAL ARTICLE
15 PAGES


SHARE
Vol.2004 • No. 7 • 29 June 2004
Back to Top