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 (∗) { d d t [ x ( t ) − C ( t ) x ( α t ) ] + P ( t ) t x ( β t ) = 0 , t ≥ t 0 > 0 , t ≠ t k , x ( t k ) = b k x ( t k − ) + ( 1 − b k ) ∫ β t k t k P ( s / β ) s x ( s ) d s , k = 1 , 2 , … . Sufficient conditions are obtained for every solution of (∗) to tend to a constant as t → ∞ .