THE STABILITY OF SUPER-NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS

【摘要】 <正> The main results obtained in this paper are as follows:1. For super-neutral functional differential equations, we obtain a sufficient condition for the zero solution to be asymptotically stable, as mentioned in Theorems 1, 2, 3 and have generalized the corresponding results given in [1] and [2].2. The notion about strong asymptotic stability is established and a comparison theorem is obtained.3. By means of the local Lipschitz condition, a rather simple method for finding the function p(s) is obtained. We have overcome the difficulties pointed out in [ 5 ] and [ 2 ]. Hence we have created some favourable conditions for converting the stability problems of functional differential equations to those of ordinary differential equations.更多还原

【Abstract】 The main results obtained in this paper are as follows:1. For super-neutral functional differential equations, we obtain a sufficient condition for the zero solution to be asymptotically stable, as mentioned in Theorems 1, 2, 3 and have generalized the corresponding results given in [1] and [2].2. The notion about strong asymptotic stability is established and a comparison theorem is obtained.3. By means of the local Lipschitz condition, a rather simple method for finding the function p(s) is obtained. We have overcome the difficulties pointed out in [ 5 ] and [ 2 ]. Hence we have created some favourable conditions for converting the stability problems of functional differential equations to those of ordinary differential equations.更多还原