摘要
本文研究了二阶线性立型泛函微分方程d^2/dt^2[x(t)-c(t)x(t-r)]+p(t)x(g(t))=0的非振动解的渐近性态。其中r>0为常数,c(t)∈c([t_o,+∞),(0,1)),p(t)∈c([t_o,+∞),R^+),g(t)∈c([t_o,+∞),R)且g(t)≤f,我们得到了当c(t)=c,(0<c<1)时,的任一非振动解当t→+∞时,要么趋于∞,要么趋于某有限数。该结果是文[3]相应结果的改进与推广。
In this paper, we studied the asymptotic properties of the nonoscillation solutions of the neutral functional differential equation d^2/dt^2[x(t)-c(t)x(t- r)]+p(t)x(g(t))=0. (*)Where r is a positive constant and c(t)∈c((t_o,+∞), (0, 1)), p(t)∈c((t_o, +∞),R^+),g(t)∈c((t_o, +∞),R),g(t)≤t and (t)=+∞. We obtained that if c(t)=c and 0<c<1, then any nonoscillatory solution of E_q(*) either tend to ∞, or tend to a finite constant when t→+∞.
出处
《数学杂志》
CSCD
北大核心
1989年第4期449-456,共8页
Journal of Mathematics
基金
国家自然科学基金课题
