CAJ | 학술논문

考虑变元x约束在闭区域 -Ω上的微分包含的初值问题.对给定的有约束微分包含x'∈F(t,x)的初值问题x(to)=xo 的一个定义在[to,+∞)的AC解及任意的点yo ∈-Ω,证明了存在一个该约束微分包含的满足初始条件yo的定义在[to,+∞)的PC解y(·)且满足|x(t)-y(t)|≤Ceξ(t-to)|xo-yo|,这里F满足单边Lipschitz条件,Ω满足一致内球条件.
고필변원x약속재폐구역 -Ω상적미분포함적초치문제.대급정적유약속미분포함x'∈F(t,x)적초치문제x(to)=xo 적일개정의재[to,+∞)적AC해급임의적점yo ∈-Ω,증명료존재일개해약속미분포함적만족초시조건yo적정의재[to,+∞)적PC해y(·)차만족|x(t)-y(t)|≤Ceξ(t-to)|xo-yo|,저리F만족단변Lipschitz조건,Ω만족일치내구조건.
The initial value problem of the differential inclusion x'∈F(t,x) is investigated,wherethe variable x is constrained to a closed domain -Ω.It is shown that given yo ∈-Ω and an AC solution x |x(t)-y(t)|≤Ceζ(t-to)|xo-yo|,when F is one-side Lipschitz continuous.Ω satisfies the Uniform Internal Sphere Condition.