微分包含的周期解的存在性定理

On the existence theorem of periodic solution for differential inclusion

讨论了微分包含x(t)∈F(t,x(t))在凸和非凸两种情况下的周期解存在性定理,当F(t,x(t))满足单边Lipschitz条件,且非凸、下半连续和凸、上半连续时,使用Leray-Schauder替换定理,分别证明了凸和非凸两种情况下的存在性定理.

The authors study the existence of periodic solution for differential inclusion x＇（t）∈F（ t, x （t）） under the hypothese both convex and nonconvex problem. Using Leray - Schauder ahemative theorem, we obtain the existence theorem when F（ t ,x（t）） satisfy one -side Lipschitz condition under nonconvex lower- semicontinuous and convex upper - semicontinuous