具有正负系数的连续变量的差分方程解的零点分布

DISTRIBUTION OF ZEROS FOR DIFFERENCE EQUATIONS WITH CONTINUOUS ARGUMENT AND POSITIVE AND NEGATIVE COEFFICIENTS

考虑具有正负系数的连续变量的差分方程 x(t)-x(t-γ)+P(t)x(t-τ)-Q(t)x(t-σ)=0,其中P,Q∈C([t_0,∞),R^+),τ,σ,γ∈(0,∞)。本文给出了上述方程解的零点分布及方程所有解振动的充分条件并改进和推广了已有的结果。

Consider the difference equation In this paper, some estimates of distance between adjacent zeros of solutions and sufficient conditions for oscillation of above equation are obtained; This result improves and developes some known results.