Asymptotic behavior of solutions of nonlinear impulsive delay differential equations with positive and negative coefficients

Abstract

This paper is concerned with the nonlinear impulsive delay differential equations with positive and negative coefficients (*) { x ′ ( t ) + p ( t ) f ( x ( t − τ ) ) − q ( t ) f ( x ( t − σ ) ) = 0 , t ≥ t 0 , t ≠ t k , x ( t k ) = b k x ( t k − ) + ( 1 − b k ) ( ∫ t k − τ t k p ( s + τ ) f ( x ( s ) ) d s − ∫ t k − σ t k q ( s + σ ) f ( x ( s ) ) d s ) , k = 1 , 2 , 3 , … . Sufficient conditions are obtained for every solution of equation (*) tending to a constant as t → ∞ .