New oscillatory criteria for higher-order nonlinear neutral delay differential equation

In this paper, we consider the higher-order nonlinear neutral delay differential equation (1.1) ( x ( t ) − p ( t ) x ( t − τ ) ) ( n ) + f ( t , x ( σ ( t ) ) ) = 0 where n is an odd number and n ⩾ 3 , τ > 0 , p , σ ∈ C ( [ t 0 , ∞ ) , R + ) , σ ( t ) ⩽ t , lim t → ∞ σ ( t ) = ∞ , f ∈ C ( [ t 0...

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Bibliographic Details
Published in:Nonlinear analysis 2008-09, Vol.69 (5), p.1719-1731
Main Authors: Liang, Haiyan, Li, Qiaoluan, Zhang, Zhenguo
Format: Article
Language:English
Subjects:
Delay
Exact sciences and technology
Mathematical analysis
Mathematics
Neutral differential equation
Ordinary differential equations
Oscillation
Sciences and techniques of general use
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Summary:In this paper, we consider the higher-order nonlinear neutral delay differential equation (1.1) ( x ( t ) − p ( t ) x ( t − τ ) ) ( n ) + f ( t , x ( σ ( t ) ) ) = 0 where n is an odd number and n ⩾ 3 , τ > 0 , p , σ ∈ C ( [ t 0 , ∞ ) , R + ) , σ ( t ) ⩽ t , lim t → ∞ σ ( t ) = ∞ , f ∈ C ( [ t 0 , ∞ ) × R , R ) , f ( t , u ) is nondecreasing in u .
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2007.07.018