集值微分方程是一类可用于描述和解决具有不确定性特征的复杂的非线性系统，并被广泛应用于科学和技术领域。常微分方程，多值微分包含和模糊微分方程等可视为其特殊情况。.本项目将以集值微分方程为主要研究对象，利用集值分析理论、非光滑分析、稳定性理论，通过类-Lyapunov函数（泛函）、比较原理、积分微分不等式、改进的单调迭代技术、拟线性化和计算机模拟等方法，对几类集值微分方程和Fréchet空间上集值微分方程的可解性、稳定性及收敛性等问题进行深入研究，得到Fréchet空间上集值微分方程极值解的存在性，解与近似解的误差估计，具有时滞、不确定参数、不同初始时刻变化等影响的各类集值微分方程解和层解的各类稳定性以及解的快速收敛性结果。完善和发展集值微分系统理论。本项目工作的开展既重视研究成果，也重视方法的改进、统一和扩展。

Set differential equations is a type of complicated nonlinear dynamic system which can be used to describe and solve uncertain problems, and widely used in the fields of science and technology. Ordinary differential equations, multi-valued differential inclusion and fuzzy differential equations are regarded as special cases of the system..On the basis of the existing researches, this project attempts to focus on the solvability, all sorts of stability and the fast convergence of the solutions of set differential equations and set differential equations in Fréchet Space. It aims at not only obtaining the existence of extremal solutions, the error estimate between the solutions and approximate solutions in Fréchet Space, but also giving criteria for all sorts of stability and the fast convergence of the solutions and sheaf solutions for each type of set differential equations with delay, uncertain parameters and initial time difference by employing the Lyapunov-like functions(functional), comparison principle, differential and integral inequalities, generalized monotone iterative techniques and quasilinearization, computer simulation and so on. The theoretical bases of this project include set valued analysis theory, nonsmooth analysis, stability theory. It tries to improve the theories of set differential system, to propose more applicable results of the studies and to achieve new breakthroughs in the approaches to the problem. This project values not only the research result, but also the improvement, unity and expansion of the methods.