In this paper, we study existence of mild solutions for a second order impulsive neutral functional differential equations with state-dependent delay. By using a fixed point theorem for condensing maps combined with theories of a strongly continuous cosine family of bounded linear operators, we prove the main existence theorems. As applications of these obtained results, some practical conseque...

In this paper, we investigate the existence of solutions for a class initial value problems impulsive Caputo-Hadamard fractional differential equations with state-dependent delay.

For the second order linear impulsive differential equation with oscillatory coefficient ⎧⎨ ⎩ (r(t)x′(t))′ +h(t)x(t) = 0, t = tk, tk t0, k = 1,2, · · · , x(t+ k ) = akx(tk), x ′(t+ k ) = bkx ′(tk), k = 1,2, · · · , x(t+ 0 ) = x0, x ′(t+ 0 ) = x ′ 0, (E) where h can be changed sign on [t0,∞) , by using the equivalence transformation, we establish an associated impulsive differential equation wit...

In this paper, we investigate the impulsive stabilization of certain delay differential equations with piecewise constant argument by using Lyapunov function and analysis methods. Some nonimpulsive systems can be stabilized by imposition of impulsive controls. We also give an example to demonstrate the effectiveness of the proposed control and stabilization methods. AMS Subject Classifications:...

This paper studies linear impulsive systems with varying time-delay and uncertainty. By using the method of the variation of constants formula for impulsive system, robustly global exponential stability criteria are established in terms of fairly simple algebraic conditions. Estimate of the decay rate of the solutions of such systems are also derived. Some examples are given to illustrate the m...

In this paper, a class of impulsive difference equations with time-varying delays is considered. By establishing an impulsive delay difference inequality, some sufficient conditions ensuring all solutions either oscillate or tend to zero are obtained. An example is given to illustrate the feasibility of the obtained result. AMS Subject Classifications: 34K15, 34K10.