具有正负系数的脉冲微分方程的振动性

Oscillation of Impulsive Differential Equation with Positive and Negative Coefficients

研究具有正负系数的脉冲时滞微分方程{[x(t)-R(t)x(t-r)]′+P(t)x(t-τ)-Q(t)x(t-σ)=0,t≥t0,x(tk^+)=bkx(tk),k=1,2,…解的振动性.其中R(t),P(t),Q(t)∈PC([t0,∞),R^+),r>0,τ≥0,σ≥0是某些常数,tk和bk是满足一定条件的实序列.

This paper studies the oscillation properties of the solutions to the impulsive delay differential equation with positive and negative coefficients{[x(t)-R(t)x(t-r)]′+P(t)x(t-τ)-Q(t)x(t-σ)=0,t≥t 0,x(tk^+)=b kx(tk),k=1,2,…,where R(t),P(t),Q(t)∈PC([t 0,∞),R^+).r>0,τ≥0,σ≥0 are some constants,tk and b k are real sequences satisfying certain conditions.