New oscillation theorems for a class of second-order damped nonlinear differential equations

2012 ◽  
Vol 63 (9) ◽  
pp. 1441-1457 ◽  
Author(s):  
E. Tunç ◽  
H. Avcı
Keyword(s):  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
Second Order ◽  
Oscillation Theorems

scholarly journals Oscillation theorems for second order nonlinear differential equations with deviating arguments

1987 ◽  
Vol 10 (1) ◽  
pp. 35-45 ◽  
Author(s):  
S. R. Grace ◽  
B. S. Lalli
Keyword(s):  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
Second Order ◽  
Oscillatory Behaviour ◽  
Deviating Arguments ◽  
Oscillation Criteria ◽  
Oscillation Theorems

New oscillation criteria for the oscillatory behaviour of the differential(a(t)x·(t)) ·+p(t)x·(t)+q(t)f(x[g(t)])=0                ,( · =ddt)and(a(t)ψ(x(t))x·(t)) ·+p(t)x·(t)+q(t)f(x[g(t)])=0,are established

scholarly journals Linearization and Higher Order Nonlinear Oscillation Theorems Using Comparison Methods

2004 ◽  
Vol 11 (1) ◽  
pp. 7-26
Author(s):  
Ravi P. Agarwal ◽  
Said R. Grace ◽  
Donal O'Regan
Keyword(s):  
Differential Equations ◽  
Nonlinear Oscillation ◽  
Nonlinear Differential Equations ◽  
Main Idea ◽  
Higher Order ◽  
Second Order ◽  
Oscillation Criteria ◽  
Second Order Differential Equations ◽  
Comparison Methods ◽  
Oscillation Theorems

Abstract We establish some new oscillation criteria for higher order nonlinear differential equations. The main idea involves comparing our equation with the related linear second order differential equations so that the known oscillation theorems from the literature can be employed directly.

scholarly journals Oscillation Theorems for Second-Order Damped Nonlinear Differential Equations

2009 ◽  
Vol 2009 ◽  
pp. 1-15
Author(s):  
Hui-Zeng Qin ◽  
Yongsheng Ren
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
Second Order ◽  
Oscillation Criteria ◽  
Oscillation Theorems

We present new oscillation criteria for the differential equation of the form , where , . Our research is different from most known ones in the sense that H function is not employed in our results, though Riccati's substitution and its generalized forms are used. Our criteria which are established under quite general assumptions are an extension for previous results. In particular, by taking , the above-mentioned equation can be reduced into the various types of equations concerned by people currently.

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