反序上下解条件下二阶多点边值问题

Second-order Multiple-point Boundary Value Problems with Upper and Lower Solutions in the Reverse Order

利用反序上下解方法研究二阶多点边值问题,当算子F映序区间入序区间时,证明该算子不动点的存在性.引入增算子,给出单调迭代序列,证明了最大解和最小解的存在性,并运用压缩映像原理讨论解的唯一性.

In this paper, we discuss the second-order multiple-point boundary value problems with upper and lower solutions in the reversed order. We get the existence of the maximal solution and the minimal solution by introducing an increasing operator and giving a monotone iterative sequence. The uniqueness is proved by using the contraction mapping principle.