Oscillation of second-order nonlinear dynamic equations with positive and negative coefficients

The paper considers the oscillation of a second-order nonlinear dynamic equation with positive and negative coefficients of the form [ r ( t ) x Δ ( t ) ] Δ + p ( t ) f ( x ( ξ ( t ) ) ) − q ( t ) h ( x ( δ ( t ) ) ) = 0 on an arbitrary time scale T . We obtain some oscillation criteria for the equa...

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Bibliographic Details
Published in:Advances in difference equations 2013-06, Vol.2013 (1), p.168-168, Article 168
Main Authors: Chen, Da-Xue, Qu, Pei-Xin, Lan, Yong-Hong
Format: Article
Language:English
Subjects:
Analysis
Difference and Functional Equations
Functional Analysis
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
Partial Differential Equations
Progress in Functional Differential and Difference Equations
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Summary:The paper considers the oscillation of a second-order nonlinear dynamic equation with positive and negative coefficients of the form [ r ( t ) x Δ ( t ) ] Δ + p ( t ) f ( x ( ξ ( t ) ) ) − q ( t ) h ( x ( δ ( t ) ) ) = 0 on an arbitrary time scale T . We obtain some oscillation criteria for the equation by developing a generalized Riccati substitution technique. Our results extend and improve some known results in the literature. Several examples are given to illustrate our main results. MSC: 39A10, 34N05.
ISSN:1687-1847
1687-1847
DOI:10.1186/1687-1847-2013-168