一类隐式模糊微分方程解的存在唯一性  

Existence and Uniqueness of Solutions of Implicit Fuzzy Differential Equations

作　　者：郭元伟[1] 吕振伟[1] GUO Yuanwei;LV Zhenwei(Department of Mathematics,Taiyuan Institute,Taiyuan 030032,Shanxi,China)

机构地区：[1]太原学院数学系,山西太原030032

出　　处：《山西师范大学学报（自然科学版）》2024年第2期1-8,共8页Journal of Shanxi Normal University(Natural Science Edition)

基　　金：山西省高等学校科技创新项目(2022L581);太原学院级一般科研项目(21TYKY03).

摘　　要：研究了隐式模糊微分方程初值问题和边值问题x′(t)=f(t,x(t),x′(t)),t∈[0,T]{x(0)=x_(0),x_(0)∈E和x′(t)=f(t,x(t),x′(t)){x(0)=λx(T),x(0)∈E的解的存在唯一性.基于强广义微分给出隐式模糊微分方程的积分等价形式,利用广义压缩映射原理证明解的存在唯一性,最后给出了具体的算例验证其合理性.In this paper,we study the existence and uniqueness of solutions for the following implicit fuzzy differential equation initial value problem and boundary value problem.x′(t)=f(t,x(t),x′(t)),t∈[0,T]{x(0)=x_(0),x_(0)∈Eandx′(t)=f(t,x(t),x′(t)){x(0)=λx(T),x(0)∈E Based on the strong generalized differential,the integral equivalent form of implicit fuzzy differential equation is given,and the existence and uniqueness of the solution is proved by using the principle of generalized contractive mapping.Finally,a specific example is given to verify its rationality.

关 键 词：强广义微分 模糊微分方程 初值问题 边值问题 

分 类 号：O159[理学—数学]