Abstract
The oscillation of impulsive differential equations plays an important role in many applications in physics, biology and engineering. The symmetry helps to deciding the right way to study oscillatory behavior of solutions of impulsive differential equations. In this work, several sufficient conditions are established for oscillatory or asymptotic behavior of second-order neutral impulsive differential systems for various ranges of the bounded neutral coefficient under the canonical and non-canonical conditions. Here, one can see that if the differential equations is oscillatory (or converges to zero asymptotically), then the discrete equation of similar type do not disturb the oscillatory or asymptotic behavior of the impulsive system, when impulse satisfies the discrete equation. Further, some illustrative examples showing applicability of the new results are included.
Highlights
Calogero VetroAs is well known, impulsive differential equations serve as basic models to study the dynamics of processes that are subject to sudden changes in their states
Impulsive differential equations serve as basic models to study the dynamics of processes that are subject to sudden changes in their states
We use the concept of symmetry slightly to study the oscillation criteria of neutral impulsive differential equations
Summary
Impulsive differential equations serve as basic models to study the dynamics of processes that are subject to sudden changes in their states. We use the concept of symmetry slightly to study the oscillation criteria of neutral impulsive differential equations. In [3], the authors established some new oscillation criteria for first order impulsive neutral delay differential systems of the form (ν(λ) − p(λ)ν(λ − δ))0 + q(λ)ν(λ − ς 1 ) − q2 (λ)ν(λ − ς 2 ) = 0, ς ≥ δ > 0. In [8], Tripathy and Santra studied oscillatory behavior for the solutions of the following forced nonlinear neutral impulsive differential systems (r (λ)(u(λ) + p(λ)ν(λ − δ))0 )0 + q(λ) g(u(λ − ς)) = h(λ), λ 6= φι , ι ∈ N (8). In this article we establish new sufficient conditions for oscillation and non-oscillation properties of solutions to the following impulsive system r (λ) ν(λ) + p(λ)ν(δ(λ)).
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
