二阶线性中立时滞方程非振动解的存在性

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.

EXISTENCE OF NONOSCILLATORY SOLUTION OF SECOND ORDER LINEAR NEUTRAL DELAY EQUATION

Conside the neutral delay differential equation with positive and negative coefficients \ \frac{d^{2}}{dt^{2}}x(t)+px(t-\tau )]+Q_{1}(t)x(t-\sigma _{1})-Q_{2}(t)x(t-\sigma _{2})=0, \] where $p\in R$ and $\tau \in (0,\infty ),\sigma _{1,}\sigma _{2}\in \lbrack 0,\infty )$ and $Q_{1},Q_{2}\in C(t_{0},\infty ),R^{+}).$Some sufficent conditions for the existence of a nonoscillatory solution of the above equation express in the terms of $\int\limits_{{}}^{\infty}sQ_{i}{\rm d}s<\infty,i=1,2,$are obtained, theseresults delete a rather strong assumption in 1],and improve some theorems in 1].