Existence and Uniqueness Theorem for the Cauchy Problem of Fuzzy Differential Equations under Non-Lipschitz Conditions

Solutions of fuzzy differential equations provide a noteworthy example of time-dependent fuzzy sets The purpose of this paper is to introduce functions of a suitable Lyapunov-like type and to show the existence and uniqueness theorem for the Cauchy problem of fuzzy differential equations under non-Lipschitz conditions The comparison principles and the existence and uniqueness theorems of this paper generalize many well-known results up to now

模糊弹粘塑性问题及其解的唯一性和存在性

本文基于模糊集提出了模糊弹粘塑性力学问题。为使模糊屈服面明朗化,文中引入了与模糊集截集相应的模糊屈服函数族。并巧妙地将隶属函数和屈服函数联系起来。在模糊集下的闭凸集意义上,给出了模糊弹粘塑性问题的变分表述,进而论述了问题解的唯一性和存在性。