Oscillation criteria of second-order half-linear dynamic equations on time scales

In this paper, by using the Riccati transformation technique, chain rule and inequality A λ - λ AB λ - 1 + ( λ - 1 ) B λ ⩾ 0 , λ > 1 , where A and B are positive constants, we will establish some oscillation criteria for the second-order half-linear dynamic equation ( p ( t ) ( x Δ ( t ) ) γ ) Δ...

Full description

Saved in:
Bibliographic Details
Published in:Journal of computational and applied mathematics 2005-05, Vol.177 (2), p.375-387
Main Author: Saker, S.H.
Format: Article
Language:English
Subjects:
Exact sciences and technology
Finite differences and functional equations
Mathematical analysis
Mathematics
Ordinary differential equations
Oscillation
Sciences and techniques of general use
Second-order half-linear dynamic equations
Time scale
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this paper, by using the Riccati transformation technique, chain rule and inequality A λ - λ AB λ - 1 + ( λ - 1 ) B λ ⩾ 0 , λ > 1 , where A and B are positive constants, we will establish some oscillation criteria for the second-order half-linear dynamic equation ( p ( t ) ( x Δ ( t ) ) γ ) Δ + q ( t ) x γ ( t ) = 0 , t ∈ [ a , b ] on time scales, where γ > 1 is an odd positive integer. Our results not only unify the oscillation of half-linear differential and half-linear difference equations but can be applied on different types of time scales and improve some well-known results in the difference equation case. Some examples are considered here to illustrate our main results.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2004.09.028