一类二阶微分方程的上下解方法

Upper and lower solutions for a second order differential equation

讨论二阶非线性微分方程. 假定相关问题上下解是良序的, 也就是说, 上解比下解大. 通过用一列非奇异问题且利用这一列问题算子拓扑度与上下解的关系, 去逼近本文所讨论的奇异初值边界问题, 得到解的存在结果.

This paper deals with the second-order nonlinear di?erential equation. Provided existence of upper and lower solutions of the problems which are well-ordered, we approximate our singular problem by a sequence of nonsingular problems and use the relation between the topological degree of the operator associated to the above problems and the strict upper and lower solutions, in order to obtain our existence results.