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 - delta)) = 0, t not equal 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. (C) 2009 Published by Elsevier B.V.