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Nonlinear oscillation of second‐order neutral dynamic equations with distributed delay
Author(s) -
Yang Qiaoshun,
Jia Baoguo,
Xu Zhiting
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3469
Subject(s) - oscillation (cell signaling) , dynamic equation , nonlinear system , mathematics , order (exchange) , constant (computer programming) , control theory (sociology) , mathematical analysis , physics , computer science , quantum mechanics , control (management) , finance , artificial intelligence , economics , programming language , genetics , biology
In this paper, we consider the nonlinear oscillation of the following second‐order neutral delay dynamic equations with distributed delayr ( t ) | Z Δ ( t ) | α − 1Z Δ ( t )Δ + ∫ c d q ( t , ξ ) | x ( θ ( t , ξ ) ) | β − 1 x ( θ ( t , ξ ) ) Δξ = 0on a time scale T , where Z ( t ) = x ( t ) + p ( t ) x ( τ ( t )), α , β > 0 are constants. By using some new techniques, we obtain oscillation criteria for the equation when β > α , β = α , and β < α , respectively. Those results established here complete and develop the oscillation criteria in the literature. Also, our main results are illustrated with some examples. Copyright © 2015 John Wiley & Sons, Ltd.