时间测度上二阶多点边值问题正解的存在性  

Existence of Positive Solutions to Multi-point Boundary Value Problem of Second-order Differential Equations on Time Measure

作　　者：范进军[1] 孙茂菁[1] 

机构地区：[1]山东师范大学数学科学学院,济南250014

出　　处：《工程数学学报》2014年第3期381-386,共6页Chinese Journal of Engineering Mathematics

基　　金：山东省自然科学基金(ZR2009AM006)~~

摘　　要：时间测度上微分方程的多点边值问题可以精确描述许多重要的物理现象,有着广泛的实际应用背景.本文研究时间测度上一类二阶非线性动力方程多点边值问题正解的存在性.我们首先论证时间测度上二阶微分方程多点边值问题等价于某个积分方程的求解问题;其次,构造一个特殊的锥和锥上的特殊泛函以及一个特殊的积分算子;最后,利用锥上的不动点定理,证明了二阶非线性动力方程多点边值问题至少有两个正解.对于差分方程和微分方程两种特殊情况,所得结果也是新的结论.Multi-point boundary value problems of differential equations on time measure can accurately describe a number of important physical phenomena and have a broad application background.In this paper,we study the existence of positive solutions to multi-point boundary value problems of a class of second-order nonlinear dynamic equation on time measure.Firstly,we prove that the multi-point boundary value problem of second-order differential equations on time measure is equivalent to solving an integral equation; Secondly,we construct a special cone and some special functionals on the cone as well as a special integral operator; Finally,by using the fixed point theorem on cone,we obtain at least two positive solutions to the multi-point boundary value problems of the second-order nonlinear dynamic equation on time measure.For two special cases,difference equations and differential equations,our result is also new.

关 键 词：正解 边值问题 锥 时间测度 不动点定理 

分 类 号：O175.8[理学—数学]