The Persistence of Oscillation and Asymptotic Behavior for Impulsive Differential Equations

Consider the impulsive differential equation of neutral type (1) { [ x ( t ) + p x ( t − τ ) ] '   + Q ( t ) x ( t − σ ) = 0 ,   t   ⩾   0 ,   t ≠ t k x ( t k + ) − x ( t k − ) = b k [ x ( t k − ) + p x ( t k − τ ) ] ,   k = 1 , 2 , ⋯ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003067498/6ba0c26b-f086-40cc-86ed-1693dc596221/content/eq3180.tif"/>