Equivalence of the Oscillation of Two Coupled Differential Systems

摘要

In this paper, we establish the equivalence of the oscillation of the following two coupled differential systems [xi(t)-xi(t-τi)]'+pi(t)fi(x1(t-τi1),…,xn(t-τin))=0 for i =1,…,n and yi''(t)+pi(t)/τi fi(y1(t),…yn(t))=0 for i=1,…,n,where pi(t)∈C(R+,R+),τi are nonnegative real num-bers, τij for i,j=1,…,n are real numbers, fi (u1,…,un)is nondecreasing in ui for i=1,…,n and satisfies the following conditions fi(u1…,un)>0 if ui> 0 for i=1,…,n,fi(u1…,un)＜0 if ui＜0 for i=1,…,n.