On certain comparison theorems for half-linear dynamic equations on time scales
type: Item
instance of: scholarly article
title: On certain comparison theorems for half-linear dynamic equations on time scales
zbMATH Open document ID: 1068.34031
DOI: 10.1155/S1085337504306251
published in: Abstract and Applied Analysis
publication date: 2005-04-29T00:00:00Z
full work available at URL: https://eudml.org/doc/51504
review text: Summary: We obtain comparison theorems for the second-order half-linear dynamic equation \[ [r(t)\Phi(y^\Delta)]^\Delta+ p(t)\Phi(y^\sigma)= 0, \] where \(\Phi(x)=|x|^{\alpha-1}\text{sgn\,}x\) with \(\alpha> 1\). 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 \(\alpha\) in the nonlinearity \(\Phi\), under certain assumptions. Moreover, we give a generalization of the 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.
Mathematics Subject Classification ID: 34C10
Mathematics Subject Classification ID: 39A10
zbMATH DE Number: 2163673
zbMATH Keywords: time scales comparison theorems
author: Pavel Rehak
MaRDI profile type: Publication
OpenAlex ID: W2169485385
description: scientific article; zbMATH DE number 2163673