非凸性条件下二阶微分包含解的存在性

Solution of Three-point Boundary Value Problems for Second Order Differential Inclusions

多值微分方程是非线性分析理论的一个重要分支,它在工程、经济、最优控制及最优化理论等领域有着广泛的应用.因此,对多值微分方程的研究具有重要意义.本文在有限维空间R上,借助于Bressan-Colom-bo连续选择定理和Schauder不动点定理,在多值函数非凸值的情形下建立了二阶多值微分方程三点边值问题x″∈F(t,x,x)′,a.e.t∈[0,1]x(′0)=0,x(1)=αx(ηη)(1.1)解的存在性,其中F是一个满足L1-Caratheodory条件的多值函数,α≠1,0<η<1.

Multivalued functional differential equations are an important branch in the theory of nonlinear analysis,which have wide applications in many fields such as engineering,economics,optimal control and optimization theory.Therefore,it is significant to study the existence of multivalued functional differential equations. This paper is discussed the existence of three-point boundary second order multivalued differential equation.Our main results are based upon Schauder fixed point theorem combined with a selec...