含有分布 Henstock-Kurzweil 积分的一类二阶非线性边值问题

摘要

Using the method of upper and lower solutions,in the sense of generalized derivative,we studied the existence of solutions of the second order nonlinear boundary value problems involving the distributional Henstock-Kurzweil integral.First,we introduced the definition and nature of the distributional Henstock-Kurzweil integral.Then,by the method of upper and lower solutions,we got the conclusion that operator A is progressively increase and relatively compact through three steps. Finally,we demonstrated through examples that the solutions of this kind of problem exist.%利用上下解方法，在广义导数的意义下研究含有分布 Henstock-Kurzweil 积分的二阶非线性边值问题(BVPs)解的存在性。先给出分布 Henstock-Kurzweil 积分的定义及性质，再通过上下解方法分3步证明了算子 A 递增及相对紧得到其解存在的结论，最后举例论证了该类问题解的存在性。