二阶线性中立时滞方程非振动解的存在性

EXISTENCE OF NONOSCILLATORY SOLUTION TO SECOND ORDER LINEAR NEUTRAL DELAY EQUATION

考虑具有正负系数的中立时滞微分方程这里P∈R和τ∈(0,∞),σ1,σ2∈[0,∞)且Q1,Q2∈C([t0,∞),R+).对于上面方程非振动解的存在性,得到一个用,∫sQids <∞,i=1,2,来表达的充分条件。这个结果去掉了M.R.S.Kulenovic和S.Hadziomerspahic文中一个相当强的假设,改进了其中的相关定理.

Conside the neutral delay differential equation with positive and negative coefficients where p ∈ R and τ ∈ (0,∞),σ1,σ2 ∈ [0,∞) and Q1,Q2 ∈ C([to,∞),R+).Some sufficent conditions for the existence of a nonoscillatory solution to the above equation express in the terms of ∫ sQids < ∞,i = 1,2 are obtained. These results delete a rather strong assumption in [1], and improve some theorems in [1].