中立型具正负系数的一阶时滞微分方程振动的充分必要条件

本文研究具有正负系数的一阶中立型时滞微分方程的振动性 ,建立了一切解振动的充分条件 ,该条件依据方程的系数与时滞经过若干步计算就能判定方程 (1)的振动性 ,较之文 1]更具实用性和可操作性

Necessary and Sufficient Condtions for Oscillation of First Neutral Delay Differential Equation with Positive and Negative Coefficients

Consider the neutral delay differential equation with positive and negative coefficients (x(t)+hx(t-r))′+px(t-τ)-qx(t-σ)=0(1) Where p, q, h,τ,σ are positive real numbers, We obtained explicit necessary and sufficient conditions for oscillation of Equ.(1). Using these conditions associated coefficients and delays of Equ.(1),We can verify all solution of Equ.(1) to be oscillatio by the calcalation of limited in number steps, Our results are more parctical and operational comparing with the literature in 1].