一类一阶和二阶微分方程的渐近概周期解

对于一阶微分系统u′+F(u)=h(t),其中F为R~n上的严格单调算子,本文给出了其渐近概周期解存在和唯一的一个充分条件和一个必要条件.特别,对于一阶微分系统u′+▽Φ(u)=h(t),其中▽Φ代表R~N上凸函数Φ的梯度,讨论了其渐近概周期解存在和唯一的充分必要条件,并且把一些结果推广到了一类二阶方程.

Asymptotically Almost Periodic Solutions for Some First-Order and Second-Order Differential Equations

We investigate the existence and uniqueness of asymptotically almost pe- riodic solutions for the first-order differential system:u′+F(u)=h(t),where F is a strictly monotone map on R~N.Particularly,we discuss the necessary and sufficient conditions for the existence and uniqueness of asymptotically almost periodic solutions for the first-order differential equation u′+▽Φ(u)=h(t),where▽Φdenotes the gradi- ent of the convex functionφon R~N.Then we extend the results to some second-order equations.