Abstract
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, where β > α > 0, z(t) = x(t) + λ(t)x(τ(t)). Several oscillation criteria for the above equation are established in both the case 0 ≤ λ(t) ≤ 1 and 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.
Highlights
We investigate the oscillation of a class of second-order subhalf-linear neutral impulsive differential equations of the form r t φβ z t p t φα x σ t
Impulsive differential equations appear as a natural description of observed evolution phenomena of several real-world problems involving thresholds, bursting rhythm models in medicine and biology, optimal control models in economics, pharmacokinetics, and frequency modulates systems 1–5
Impulsive differential equations have received a lot of attention
Summary
Impulsive differential equations appear as a natural description of observed evolution phenomena of several real-world problems involving thresholds, bursting rhythm models in medicine and biology, optimal control models in economics, pharmacokinetics, and frequency modulates systems 1–5. Two examples are given to illustrate the effect of impulses on the oscillatory behavior of solutions to the equation. For the general sub-halflinear neutral equation 1.1 under the impulse condition given in this paper, little has been known about the oscillation of 1.1 to the best of our knowledge, especially for the case when −1 < −μ ≤ λ t ≤ 0.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
