两端简单支撑的奇异梁方程的正解  

Existence of Positive Solution to Singular Beam Equations Simply Supported at Both Ends

作　　者：姚庆六[1] 

机构地区：[1]南京财经大学应用数学系,南京江苏210003

出　　处：《数学进展》2009年第5期590-598,共9页Advances in Mathematics（China）

基　　金：国家自然科学基金(No.10571085)

摘　　要：证明了一类非线性四阶两点边值问题的一个正解存在定理.允许非线性项在时间变元t=0,t=1及状态变元u=0处奇异.主要工具是全连续算子序列的逼近方法和锥拉伸与锥压缩型的Guo-Krasnosel'skii不动点定理.在力学上这一问题描述了两端简单支撑的弹性梁的形变.An existence theorem of positive solution is proved for a class of nonlinear fourth-order two-point boundary value problems.The singularities of nonlinear term are allowed at time variable t = 0,t = 1 and state variable u= 0.Main ingredients are the approximation method of completely continuous operators and the Guo-Krasnosel skii fixed point theorem of cone expansion-compression type.In mechanics,the class of problems describes the deformation of an elastic beam simply supported at both ends.

关 键 词：常微分方程 边值问题 奇异性 正解 存在性 

分 类 号：O175.8[理学—数学]