Asymptotic Stability And Exponential Stability Of Differential Equations

This paper mainly discuss the stability of the solutions of differential equa-tions.Firstly,we investigate the following neutral differential equation with un-bounded delaySome theorems are established for the solution of this equation to be uniformly stable and asymptotical stable.Secondly,the asymptotical stability of the solu-tions of the neutral differential equationis investigated by means of fixed point theory,where bj(t)∈C([to, ,∞). R), aj(t)∈C([to,∞), R+),with t - aj(t)→∞as t→∞.Third,consider the impulsive delay differential equation of the formwhere wc establish some exponential stability by use of Razumikhin methods. Finally,consider the impulsive delay differential equation of the form whereσ≥> to,φ∈PCB([α,0],Rn)impulse times tk satisy denotes the right-hand derivative of x, is an open set in PC([α,0],Rn),we develop the weak exponential stability and exponential stability by means of Razumikhin technique.