We studied the bifurcation properties of stationary points of a class of planar piecewise smooth system with 3 parameters using the theory of differential inclusions,presenting both sufficient and neccesary conditions of the existence of the stationary points in this class of planar piecewise smooth systems.

We studied the bifurcation of equilibria of a planar piecewise smooth system when the discontinuity and the equilibria interact on each other.

The stability of homoclinic cycles in planar piecewise smooth systems was studied.

A new method is obtained for a special nondifferentiable problem——piecewise smooth optimi- zation.

Defines bordered manifold and concordantly oriented concepts of smooth or piecewise smooth bordered manifold, thus proof“general Stokes formula by n-demensional E-G formula.

The paper aims to obtained a new method for a special nondifferentiable problem, Piecewise smooth optimization,and applys it to multiobjective programming to get a new minmax method.

An efficient variation-based algorithm for computing the largest Lyapunov exponent of a class of piecewise smooth systems-DC/DC converters is derived, which takes the advantages of the variational algorithm and Mu ller method.

Based on the sequence of circuit topologies, a symbolic sequence method is proposed for analyzing the bifurcations and chaos in a class of piecewise smooth systems like DC/DC converters.

In this paper, the author considers the discontinuous initial boundary value problem for the one-dimensional semilinear wave equation originated from semi-bounded string vibration, and proves the global existence theorem of piecewise smooth solutions to this problem by using the method of characteristic.

Optimal Control and Stability of Nonlinear Piecewise Smooth Dynamical Systems;