时标上一类时滞中立型动力方程的非振动解

Nonoscillatory Solutions for One Netural Dynamic Equation on Measure Chains

考虑了时标上时滞中立型动力方程(x(t)-cx(t-τ))~Δ+q(t)x(t-σ)=0,其中τ>0,σ≥0为常数,q(t)∈C_(rd)[T,R^+).运用压缩映射原理获得了该方程非振动解存在的充分条件.

Considering the neutral delay dynamic equations（x（t）-cx（t-τ））^Δ＋q（t）x（t-σ）=0,Where q（t）∈C_（rd）[T,R＋）,and according to Contraction Mapping theorem, We obtain the sufficient condition for the existence of certain types of solutions of the above equation to be ∫t0 ∞｜q（s）｜△s〈∞.