Asymptotic behavior of solutions of a first-order impulsive neutral differential equation in Euler form

This paper is concerned with an impulsive neutral differential equation of Euler form with unbounded delays equation(∗){ddt[x(t)−C(t)x(αt)]+P(t)tx(βt)=0,t≥t0>0,t≠tk,x(tk)=bkx(tk−)+(1−bk)∫βtktkP(s/β)sx(s)ds,k=1,2,…. Sufficient conditions are obtained for every solution of (∗) to tend to a constant as t→∞t→∞.