一类带强迫项的中立型方程非振动解的渐近性

Asymptotic Behavior of Non-Oscillatory Solutions to First-Order Neutral Equations with Forcing Term

应用压缩映像原理讨论了一类带强迫项的一阶中立型微分方程非振动解的渐近性,得到了该方程的所有非振动解当t→∞时趋于零的充分条件.所得结果推广了文献[1]中带强迫项的一阶中立型微分方程所有解振动或当t→∞时趋于零或趋于±∞的充要条件的结论.

By using Banach compression-imaging principle, the authors have made a discussion over the asymptotic behavior of non-oscillatory solutions to first-order neutral differential equation with forcing term, obtaining the sufficient conditions for every non-oscillatory solutions to the equation hereinabove tends to zero when t tends to infinity （t→∞）. This finding has generalized the viewpoint that all the solutions to first-order neutral differential equation are oscillatory, and that the solutions tend to 0/±∞ when t tends to infinity.