Banach空间中含间断项的二阶非线性常微分方程周期边值问题

摘要

By using the method of upper and lower solutions and some fixed point theorems of discontinuous increasing operators, sufficient conditions to guarantee the existence of maximal and minimal solution of periodic boundary value problem for second order nonlinear ordinary differential equation with discontinuous terms in Banach space are obtained. Moreover, some recent results are generalized and improved, and these results obtained in this paper are also new for finite dimensional space.%在Banach空间中利用上下解方法与不连续增算子不动点定理,研究了含间断项和右端函数具有一阶导数项的二阶非线性常微分方程周期边值问题的最大解、最小解的存在性,推广和改进了现有的结果.而且对于有限维空间,我们获得的这些结果也都是新的.