Existence and regularity of integral solutions for nonlinear parabolic differential inclusions;

Filippov theorem for C~1-trajectories of Aubin's differential inclusions

Equivalence between control systems with complementar constraints and differential inclusions

Nonlinear Boundary Value Problems for Differential Inclusions;

Viability theory is an advanced field,in which differential inclusions are used to research the state evolutions on systems with uncertainties under constraints.

A viability theorem for the partial differential inclusions is proved and a topological property of the viability solution set for the partial differential inclusions is given.

It is mainly discussed uniformly ultimate boundedness of nonautonomous sys- tems with discontinuous right-hand sides(in the sense of Filippov solutions).

By utilizing the notion of Filippov solution,Clarke generalized gradient and nonsmooth Lyapunov stability theory,a further discuss on sliding mode control is presented for second-order systems with a nonsmooth linear Lipschitz continuous sliding surface.

The stability of the sliding mode and reaching mode were proved by the properties of Filippov solution and generalized Lyapunov theory respectively.

The problem of finite-time stability is mainly discussed with respect to a closed(not necessarily compact) invariant set for a class of nonlinear systems with discontinuous right-hand sides in the sense of Filippov solutions.

In this thesis, we mainly investigate practical stability for Filippov-type ordinary differential equations and stochastic differential equations with discontinuous coefficients,and the numerical computation for stochastic differential equations with discontinuous coefficients.