一类具有脉冲的非线性时滞微分方程解的渐进性

Asymptotic Behavior of Solutions of Nonlinear Delay Differential Equations with Impulse

研究了一类具有脉冲的二阶非线性时滞微分方程(r(t)x′(t))′-p(t)x′(t)+sum from i=1 to n qi(t)x(t-σ_i+f(t)=0,t≠t_k,x(t_k^+)-x(t_k)=a_kx(t_k),x′(t_k^+)-x′(t_k)=b_kx′(t_k),k∈Z^+的解的渐近性,并得到了一系列相关的充分条件.

This paper studies the asymptotic behavior of solutions of the seond-order non-linear delay differential equations with impulses （r（t）x′（t））′-p（t）x′（t）＋i=1∑qi（t）x（t-σi）＋f（t）=0, t≠k, x（tk^＋）-x（tk）=akx（tk）,x′（tk^＋）-x′（tk）=bkx′（tk）,k∈Z^＋ and some sufficient conditions are obtained.