一类二阶三点边值问题单调正解的存在性  

Existence of Monotone Positive Solutions to a Type of Three-point Boundary Value Problem

作　　者：刘锡平[1] 贾梅[1] 葛渭高[2] 

机构地区：[1]上海理工大学理学院,上海200093 [2]北京理工大学应用数学系,北京100081

出　　处：《应用数学学报》2007年第1期111-119,共9页Acta Mathematicae Applicatae Sinica

基　　金：上海市教委自然科学基金(05EZ52号)资助项目.

摘　　要：利用范数形式的锥上不动点定理,研究了一类二阶微分方程三点边值问题单调正解的存在性．分别给出了齐次和非齐次边界条件下的三点边值问题单调正解存在的充分条件,确定了解曲线的凹凸性,并且给出了一个应用实例．This paper studies the existence of monotone positive solutions to a type of three point boundary value problems of nonlinear second-order differential equations. By use of the stretch and compression fixed point theorem of normic form in cone, the sufficient conditions for the existence of monotone positive solutions are given to the boundary value problems with homogeneous and nonhomogeneous boundary conditions, respectively. An example is also given to illustrate the effectiveness of our results.

关 键 词：三点边值问题 锥上不动点定理 单调正解 凹凸性 

分 类 号：O175.8[理学—数学]