含有分布Henstock-Kurzweil积分的一类二阶非线性边值问题  

A Class of Second Order Nonlinear Boundary Value Problems Involving Distributional Henstock-Kurzweil Integral

作　　者：王红梅[1] 叶国菊[1] 梁兵[1] 

机构地区：[1]河海大学理学院,南京211100

出　　处：《吉林大学学报（理学版）》2015年第5期846-850,共5页Journal of Jilin University:Science Edition

基　　金：中央高校基本科研业务费专项基金(批准号:B12020128)

摘　　要：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.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 Ais progressively increase and relatively compact through three steps.Finally,we demonstrated through examples that the solutions of this kind of problem exist.

关 键 词：分布Henstock-Kurzweil积分 非线性二阶边界值问题 分布导数 上下解 

分 类 号：O177.4[理学—数学]