具有“积分小”系数的中立型方程的振动性

Oscillation in Neutral Differential Equations with “Integrally Small” Coefficients

讨论中立型方程ddt[y(t) -R(t) y(t -r) ]+P(t)y(t-τ) -Q(t)y(t-σ) =0 ( )其中P ,Q ,R∈C([t0 ,∞ ) ,R+ ) ,r >0 ,τ≥σ >0。在允许 R(t) +∫tt-τ+σQ(u)du - 1可以变号的情况下 ,得到了方程 ( )

Consider the neutral differential equation [y(t)-R(t)y(t-r)]′+P(t)y(t-τ)-Q(t)y(t-σ)=0,where P,Q, R∈C([t 0, ∞), R +), r>0, τ≥σ>0. New sufficient conditions for all solutions to be oscillatory are obtained where R(t)+∫ t t-τ+σ Q(u)du-1 is allowed to oscillate.