New interval oscillation criteria for forced second-order differential equations with nonlinear damping

2013 ◽  
Vol 7 ◽  
pp. 1239-1255 ◽  
Author(s):  
Mervan Pasic
Keyword(s):  
Differential Equations ◽  
Nonlinear Damping ◽  
Second Order ◽  
Oscillation Criteria ◽  
Second Order Differential Equations ◽  
Interval Oscillation

scholarly journals Interval oscillation criteria for certain forced second-order differential equations

2012 ◽  
Vol 28 (2) ◽  
pp. 337-344
Author(s):  
ERCAN TUNC ◽  
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Second Order ◽  
Half Line ◽  
Oscillation Criteria ◽  
Second Order Differential Equations ◽  
Interval Oscillation

By using generalized Riccati transformations and an inequality due to Hardy et al., several new interval oscillation criteria are established for the nonlinear damped differential equation... The new interval oscillation criteria are different from most known ones in the sense they are based on the information only on a sequence of subintervals of [t0, ∞), rather than on the whole half-line. Our results improve and extend the known some results in the literature.

Oscillation of second-order nonlinear differential equations with damping

2014 ◽  
Vol 64 (5) ◽  
Author(s):  
Tongxing Li ◽  
Yuriy Rogovchenko ◽  
Shuhong Tang
Keyword(s):  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
Nonlinear Damping ◽  
Second Order ◽  
Oscillation Criteria ◽  
Second Order Differential Equations ◽  
Nonlinear Anal ◽  
Oscillatory Properties

AbstractWe study oscillatory properties of solutions to a class of nonlinear second-order differential equations with a nonlinear damping. New oscillation criteria extend those reported in [ROGOVCHENKO, Yu. V.—TUNCAY, F.: Oscillation criteria for second-order nonlinear differential equations with damping, Nonlinear Anal. 69 (2008), 208–221] and improve a number of related results.

scholarly journals Fite-Wintner-Leighton-Type Oscillation Criteria for Second-Order Differential Equations with Nonlinear Damping

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Mervan Pašić
Keyword(s):  
Differential Equations ◽  
Blow Up ◽  
Sufficient Conditions ◽  
Nonoscillatory Solution ◽  
Nonlinear Damping ◽  
Second Order ◽  
Oscillation Criteria ◽  
Riccati Differential Equations ◽  
Second Order Differential Equations ◽  
Main Equation

Some new oscillation criteria for a general class of second-order differential equations with nonlinear damping are shown. Except some general structural assumptions on the coefficients and nonlinear terms, we additionally assume only one sufficient condition (of Fite-Wintner-Leighton type). It is different compared to many early published papers which use rather complex sufficient conditions. Our method contains three items: classic Riccati transformations, a pointwise comparison principle, and a blow-up principle for sub- and supersolutions of a class of the generalized Riccati differential equations associated to any nonoscillatory solution of the main equation.

scholarly journals Oscillation criteria for second order differential equations with damping

1990 ◽  
Vol 49 (1) ◽  
pp. 43-54 ◽  
Author(s):  
S. R. Grace
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Second Order ◽  
Linear Differential Equations ◽  
Nonlinear Ordinary Differential Equations ◽  
Oscillation Criteria ◽  
Second Order Differential Equations ◽  
Linear Differential

AbstractNew oscillation criteria are given for second order nonlinear ordinary differential equations with alternating coefficients. The results involve a condition obtained by Kamenev for linear differential equations. The obtained criterion for superlinear differential equations is a complement of the work established by Kwong and Wong, and Philos, for sublinear differential equations and by Yan for linear differential equations.

scholarly journals Interval Oscillation Criteria of Second Order Mixed Nonlinear Impulsive Differential Equations with Delay

2012 ◽  
Vol 2012 ◽  
pp. 1-23 ◽  
Author(s):  
Zhonghai Guo ◽  
Xiaoliang Zhou ◽  
Wu-Sheng Wang
Keyword(s):  
Differential Equations ◽  
Sufficient Conditions ◽  
Impulsive Differential Equations ◽  
Second Order ◽  
Oscillation Criteria ◽  
Nonnegative Constant ◽  
Interval Oscillation ◽  
Equations With Delay

We study the following second order mixed nonlinear impulsive differential equations with delay(r(t)Φα(x′(t)))′+p0(t)Φα(x(t))+∑i=1npi(t)Φβi(x(t-σ))=e(t),t≥t0,t≠τk,x(τk+)=akx(τk),x'(τk+)=bkx'(τk),k=1,2,…, whereΦ*(u)=|u|*-1u,σis a nonnegative constant,{τk}denotes the impulsive moments sequence, andτk+1-τk>σ. Some sufficient conditions for the interval oscillation criteria of the equations are obtained. The results obtained generalize and improve earlier ones. Two examples are considered to illustrate the main results.

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