Banach空间非线性二阶奇异微分方程m点边值问题  

Nonlinear Second order m-point Singular Boundary Value Problem in Banach spaces

作　　者：谭静静[1] 张克梅[1] 

机构地区：[1]曲阜师范大学数学科学学院,山东省曲阜市273165

出　　处：《曲阜师范大学学报（自然科学版）》2010年第2期23-34,共12页Journal of Qufu Normal University(Natural Science)

基　　金：山东省自然科学基金资助项目(ZR2009AL014)

摘　　要：应用非紧性测度的性质和广义凝聚映像的Sadovskii不动点定理,获得了Banach空间中一类含有一阶导数的非线性二阶奇异微分方程m点边值问题解的存在性结果.首先给出一些定义和引理,然后定义两个新的Banach空间和不动点算子,通过证明算子A的连续有界,以及证明(A1V)+(tt),(AV)′(t)是等度连续的,该文得到边值问题(5)至少存在一个解.In this paper, the existence of a class of m-point boundary value problem of the nonlinear second order singular differential equations containing first order derivative in Banach spaces is obtained, using the properties of non-compactness measure and Sadovskii fixed point theorem of the generalized condensing mapping. We first give some basic notations, then we define two new Banach spaces and fixed point operator. By proving A being con-tinuous and bounded, and proving （AV）（t）/1＋t,and（AV）＇（t）being equally continuous, the existence results ofboundary value problem （5） is obtained.

关 键 词：边值问题 不动点定理 锥 非紧性测度 

分 类 号：O175.8[理学—数学] O175.15[理学—基础数学]