【摘要】 本文的定理1改正了文[1]的错误并去掉原来要求导数一致有界的条件,同时也给出了局部凸拓扑向量空间中拓扑度理论的一个自然的应用;定理2则在一定条件下去掉了p_i(t),T_i(t)一致有界的条件。更多还原

【Abstract】 In this article, we corrected the proof of the main theorem of Ladas et.al and obtained the following results:Theorem Consider the differential equation:Where Pi(t) and Ti(t) are continuous such that|Pi(t)|≤Pi, |Ti(t)|≤Ti i=1,2,…,n where Pi,Ti are constants. Assume thathas a positive root.Then equation (1) has a nonosciliatory solution of the formWhere A(t) is a bounded continuous function.Theorem If Pi(t), Ti(t) are continuous functions,p1(t)≠0 and |pi(t)/p1(t)|≤pi(p1=), Assume that has a positive root. Then equation (1) has a nonoscillatory solution o! the formWhere γ(s) is a bounded continuous function.The above two theorems contain many results as their special cases.更多还原