scholarly journals New interval oscillation criteria for second-order functional differential equations with nonlinear damping

2015 ◽  
Vol 13 (1) ◽  
Author(s):  
Süleyman Öǧrekçi
Keyword(s):  
Comparison Principle ◽  
Functional Differential Equations ◽  
Type Equation ◽  
Nonlinear Damping ◽  
Lower Solution ◽  
Second Order ◽  
Oscillation Criteria ◽  
Interval Oscillation ◽  
Oscillation Problem ◽  
Functional Differential

AbstractThis paper concerns the oscillation problem of second-order nonlinear damped ODE with functional terms.We give some new interval oscillation criteria which is not only based on constructing a lower solution of a Riccati type equation but also based on constructing an upper solution for corresponding Riccati type equation. We use a recently developed pointwise comparison principle between those lower and upper solutions to obtain our results. Some illustrative examples are also provided to demonstrate our results.

scholarly journals New Oscillation Criteria for Second-Order Forced Quasilinear Functional Differential Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Mervan Pašić
Keyword(s):  
Differential Equations ◽  
Differential Operators ◽  
Functional Differential Equations ◽  
Second Order ◽  
Laplacian Operator ◽  
Oscillation Criteria ◽  
Mixed Nonlinearities ◽  
Interval Oscillation ◽  
Functional Differential ◽  
The One

We establish some new interval oscillation criteria for a general class of second-order forced quasilinear functional differential equations withϕ-Laplacian operator and mixed nonlinearities. It especially includes the linear, the one-dimensionalp-Laplacian, and the prescribed mean curvature quasilinear differential operators. It continues some recently published results on the oscillations of the second-order functional differential equations including functional arguments of delay, advanced, or delay-advanced types. The nonlinear terms are of superlinear or supersublinear (mixed) types. Consequences and examples are shown to illustrate the novelty and simplicity of our oscillation criteria.

scholarly journals Oscillation Theorems for Second-Order Quasilinear Neutral Functional Differential Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Shurong Sun ◽  
Tongxing Li ◽  
Zhenlai Han ◽  
Hua Li
Keyword(s):  
Differential Equations ◽  
Functional Differential Equations ◽  
Second Order ◽  
Neutral Functional Differential Equations ◽  
Oscillation Criteria ◽  
Functional Differential ◽  
Oscillation Theorems

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, wherez(t)=x(t)+p(t)x(τ(t)),p∈C1([t0,∞),[0,∞)), andα≥1. Our results improve and extend some known results in the literature. Some examples are also provided to show the importance of these results.

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