测度链上一类时滞微分方程组的振动准则

Oscillation Criteria For A Class of Delay Differential System on Measure Chains

考虑如下时滞微分方程组y~△i(t)=f_i(t,y_1(τ_1(t)),y_2(τ_1(t)),y_1(τ_2(t)),y_2(τ_2(t))),t≥t_0,i=1,2其中(i)f_i(t,u_1,u_2,v_1,v_2)对参数都是连续的;(ii)τ_i(t)∈C_(rd)[t_0,R^+],τ_i(t)≤t,且τ_i(t)单调不减,lim t→∞τ_i(t)=∞.获得了该方程组所有解振动的充分条件.

This paper is concerned with the following delay difference system y^△i（t）=fi（t,y1（τ1（t））,y2（τ1（t））,y1（τ2（t））,t≥t0,i=1,2 where（i）fi（t,u1,u2,v1,v2） are continuous in all arguments, and （ii）τi（t）∈Crd[t0,R^＋],τi（t）≤t,τi（t）is nondeceasing,lim t→∞τi（t）=∞ ,i=1,2.Sufficient conditions of oscillatory for the above equation are obtained.