Oscillation Theorems for Second-Order Quasilinear Neutral Functional Differential Equations

New oscillation criteria are established for the second-order nonlinear neutral functional differential equations of the form (r(t)|z′(t)|α−1z′(t))’+f(t,x[σ(t)])=0, t≥t0, where z(t)=x(t)+p(t)x(τ(t)), p∈C1([t0,∞),[0,∞)), and α≥1. Our results improve and extend some known results in the literature. So...

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Bibliographic Details
Published in:Abstract and Applied Analysis 2012-01, Vol.2012 (2012), p.875-891-658
Main Authors: Sun, Shurong, Li, Tongxing, Han, Zhen-Lai, Li, Hua
Format: Article
Language:English
Subjects:
Criteria
Differential equations
Inequality
Nonlinearity
Oscillations
Science
Studies
Theorems
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Summary:New oscillation criteria are established for the second-order nonlinear neutral functional differential equations of the form (r(t)|z′(t)|α−1z′(t))’+f(t,x[σ(t)])=0, t≥t0, where z(t)=x(t)+p(t)x(τ(t)), p∈C1([t0,∞),[0,∞)), and α≥1. Our results improve and extend some known results in the literature. Some examples are also provided to show the importance of these results.
ISSN:1085-3375
1687-0409
DOI:10.1155/2012/819342