摘要
在条件ｆ：Ｒ→Ｒ连续，单调递增，｜ｆ（ｚ）≤｜，当ｚ≠０时，ｚｆ（ｚ）＞０．研究了过ｔ－ｘ平面上任意一点（ξ，η），方程（ｘ′（ｔ）＝ｆ（ｘ＜ｎ＞（ｔ））解的存在性延拓及其性质，得出了解曲线可以“填满”整个平面的结论，以及在ｆ是局部Ｌｉｐｓｃｈｉｔｚ时，任意σ∈Ｒ，满足ｘ（σ）＝σ及对任意ξ＞η＞０，满足ｘ（ξ）＝η的解的唯一性．
Under the conditions thatf∈C(R,R),|f(z)|≤1,zf(z)>0 when z≠0,and f is monotonically increasing,the paper studies the existence and continuation and behavior of solutions of the equation x′(t)=f(x <n> (t)) across any point of the t x plane and obtains the conclusion that the curves of solutions may “fill” the whole plane. The solution satisfing x(σ)=σ for any σ∈R and satisfing x(ζ)=η for any ζ>η>0 is unique when f is local Lipschitz.
出处
《北京理工大学学报》
EI
CAS
CSCD
1997年第4期401-407,共7页
Transactions of Beijing Institute of Technology
基金
国家自然科学基金
关键词
泛函微分方程
不动点定理
存在性
唯一性
functional differential equations
fixed point theorem
existence
uniqueness
