BOUNDED OSCILLATION FOR SECOND-ORDER NONLINEAR DELAY DIFFERENTIAL EQUATIONS†
@article{Song2014BOUNDEDOF, title={BOUNDED OSCILLATION FOR SECOND-ORDER NONLINEAR DELAY DIFFERENTIAL EQUATIONS†}, author={Xia Song and Quanxin Zhang}, journal={Journal of applied mathematics \& informatics}, year={2014}, volume={32}, pages={447-454} }
Two necessary and sufficient conditions for the oscillation of the bounded solutions of the second-order nonlinear delay differential equation ( a(t)x′(t) )′ + q(t)f(x[τ(t)]) = 0 are obtained by constructing the sequence of functions and using inequality technique. AMS Mathematics Subject Classification: 34C10.
One Citation
New Oscillation Criteria for the Second Order Nonlinear Differential Equations with Damping
- Mathematics
- 2016
In this paper, we are concerned with a class of second-order nonlinear differential equations with damping term. By using the generalized Riccati technique and the integral averaging technique of…
References
SHOWING 1-10 OF 18 REFERENCES
Bounded oscillation for second order non-linear neutral delay differential equations in critical and non-critical cases
- Mathematics
- 2006
Oscillation Criteria for Second Order Nonlinear Delay Equations
- MathematicsCanadian Mathematical Bulletin
- 1973
It is the purpose of this paper to establish oscillation criteria for second order nonlinear differential equations with retarded argument. Specifically, we consider the equation 1.1 where f ∊ C[0, +…
Oscillatory Behavior of Solutions for a Class of Second Order Nonlinear Differential Equation with Perturbation
- Mathematics
- 2010
In this paper, a class of second order nonlinear differential equations with perturbation is studied. By using the generalized Riccati transformation, the integral averaging technique and the method…
Oscillation and nonoscillation criteria for half-linear second order differential equations
- Mathematics
- 2006
Oscillatory properties of the second order half-linear
differential equation are investigated. The studied equation is
viewed as a perturbation of a nonoscillatory equation of the
same form.…
An integral criterion for oscillation of linear differential equations of second order
- Mathematics
- 1978
It is proved that if for some n>2 the function x1−nAn(x), where An(x) is the n-th primitive ofa(x), is not bounded above, then the equation y″ +a(x)y = 0 oscillates.
Forced oscillation of second-order nonlinear differential equations with positive and negative coefficients
- MathematicsAppl. Math. Lett.
- 2011
Bounded oscillation for second-order nonlinear neutral difference equations in critical and non-critical states
- Mathematics
- 2008
Oscillation Theory for Second Order Dynamic Equations
- Mathematics
- 2002
Preliminaries. Introduction. Initial Value Problem, Oscillation and Nonoscillation. Continuability and Boundedness. Some Basic Results for Second Order Linear Ordinary Differential Equations. Some…