Asymptotic behavior of solutions of second-order nonlinear delay differential equations with impulses

This paper is concerned with second-order nonlinear delay differential equations with impulses of the form ( r ( t ) x ′ ( t ) ) ′ + p ( t ) x ′ ( t ) + f ( t , x ( t − δ ) ) = 0 , t ≠ t k , x ′ ( t k + ) = I k ( x ′ ( t k ) ) , x ( t k + ) = J k ( x ( t k ) ) , t = t k , k = 1 , 2 , … , t ≥ t 0 . By impulsive differential inequality and Riccati transformation, sufficient conditions of asymptotic behavior of all solutions of second-order nonlinear delay differential equations with impulses are obtained. Some examples are also inserted to illustrate the impulsive effect.