scholarly journals Kamenev type oscillation criteria for second order impulsive differential equations

2021 ◽  
Vol 26 (02) ◽  
pp. 172-183
Author(s):  
S. E. Tallah ◽  
M. M. A. Elsheikh ◽  
G. A. F. Ismail
Keyword(s):  
Differential Equations ◽  
Impulsive Differential Equations ◽  
Second Order ◽  
Oscillation Criteria ◽  
Type 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 Oscillation of Second-Order Sublinear Impulsive Differential Equations

2011 ◽  
Vol 2011 ◽  
pp. 1-11 ◽  
Author(s):  
A. Zafer
Keyword(s):  
Differential Equations ◽  
Impulsive Differential Equations ◽  
Second Order ◽  
Oscillation Criteria ◽  
Impulsive Perturbations

Oscillation criteria obtained by Kusano and Onose (1973) and by Belohorec (1969) are extended to second-order sublinear impulsive differential equations of Emden-Fowler type:x″(t)+p(t)|x(τ(t))|α-1x(τ(t))=0,t≠θk;Δx'(t)|t=θk+qk|x(τ(θk))|α-1x(τ(θk))=0;Δx(t)|t=θk=0,  (0<α<1)by considering the casesτ(t)≤tandτ(t)=t, respectively. Examples are inserted to show how impulsive perturbations greatly affect the oscillation behavior of the solutions.

scholarly journals Oscillation of Certain Second-Order Sub-Half-Linear Neutral Impulsive Differential Equations

2011 ◽  
Vol 2011 ◽  
pp. 1-10
Author(s):  
Yuangong Sun
Keyword(s):  
Differential Equations ◽  
Impulsive Differential Equations ◽  
Oscillatory Behavior ◽  
Second Order ◽  
Oscillation Criteria ◽  
Auxiliary Functions

By introducing auxiliary functions, we investigate the oscillation of a class of second-order sub-half-linear neutral impulsive differential equations of the form[r(t)ϕβ(z′(t))]′+p(t)ϕα(x(σ(t)))=0,  t≠θk,Δϕβ(z′(t))|t=θk+qkϕα(x(σ(θk)))=0,Δx(t)|t=θk=0,whereβ>α>0,  z(t)=x(t)+λ(t)x(τ(t)).  Several oscillation criteria for the above equation are established in both the case0≤λ(t)≤1and the case-1<-μ≤λ(t)≤0,which generalize and complement some existing results in the literature. Two examples are also given to illustrate the effect of impulses on the oscillatory behavior of solutions to the equation.

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