Banach空间中含有间断项的一阶周期边值问题整体解的存在唯一性

Existence and Uniqueness of Global Solutions for the First Order Periodic Boundary Value Problems of Discontinuous Equations in Banach Spaces

利用半序方法,只用上解或下解得到Banach空间中含有间断项的常微分方程一阶周期边值问题在[0,a](a>0)上整体解的两个存在唯一性结果,这两个结果是独立的新结论.

Using the theory of cones and the partial-ordered method with upper solution or lower solution, we investigate the existence and uniqueness of global solutions on interval [0,a] （0〉a）for the first order periodic boundary value problem of discontinuous ordinary differential equations in Banach space. Two existence and uniqueness results are obtained. The results are new and independent of other known results.