scholarly journals Interval oscillation criteria for forced mixed nonlinear impulsive differential equations with variable delay

2018 ◽  
Vol 75 ◽  
pp. 89-95 ◽  
Author(s):  
Xiaoliang Zhou ◽  
Wu-Sheng Wang ◽  
Ruyun Chen
Keyword(s):  
Differential Equations ◽  
Impulsive Differential Equations ◽  
Variable Delay ◽  
Oscillation Criteria ◽  
Interval Oscillation

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.

scholarly journals Interval Oscillation Criteria for Super-Half-Linear Impulsive Differential Equations with Delay

2012 ◽  
Vol 2012 ◽  
pp. 1-22 ◽  
Author(s):  
Zhonghai Guo ◽  
Xiaoliang Zhou ◽  
Wu-Sheng Wang
Keyword(s):  
Differential Equations ◽  
Impulsive Differential Equations ◽  
Second Order ◽  
Riccati Transformation ◽  
Oscillation Criteria ◽  
Nonnegative Constant ◽  
Interval Oscillation ◽  
Equations With Delay

We study the following second-order super-half-linear impulsive differential equations with delay[r(t)φγ(x′(t))]′+p(t)φγ(x(t-σ))+q(t)f(x(t-σ))=e(t),t≠τk,x(t+)=akx(t),x′(t+)=bkx′(t),t=τk, wheret≥t0∈ℝ,φ*(u)=|u|*-1u,σis a nonnegative constant,{τk}denotes the impulsive moments sequence withτ1<τ2<⋯<τk<⋯,lim k→∞τk=∞, andτk+1-τk>σ. By some classical inequalities, Riccati transformation, and two classes of functions, we give several interval oscillation criteria which generalize and improve some known results. Moreover, we also give two examples to illustrate the effectiveness and nonemptiness of our results.

Sign in / Sign up

Export Citation Format

Share Document