左端简单支撑右端被滑动夹子夹住的奇异梁方程的正解  

Positive solution to a singular beam equation simply supported at left and clamped at right by sliding clamps

作　　者：姚庆六[1] 

机构地区：[1]南京财经大学应用数学系,江苏南京210003

出　　处：《云南大学学报（自然科学版）》2009年第2期109-113,共5页Journal of Yunnan University(Natural Sciences Edition)

基　　金：国家自然科学基金资助项目(10571085)

摘　　要：利用积分方程技巧和锥上的Guo-Krasnosel'skii不动点定理研究了一类非线性四阶两点边值问题的正解存在性,其中允许非线性项f(t,u,v)在t=0,t=1及u=0,v=0处奇异.在力学上这类问题模拟了左端简单支撑右端被滑动夹子夹住的弹性梁的挠曲.由于非线性项涉及弯矩,主要结论对于梁的稳定性分析是有益的.By applying the technique of integral equation and the Guo -Krasnosel＇skii fixed point cone expansion - compression type, the existence of positive solution is studied for a class of nonlinear theorem of fourth - order two -point boundary value problems, where the nonlinear term f（ t, u, v） is allowed to be singular at t = 0, t = 1 and u = 0,v = 0. In mechanics, the class of problems describes the deflection of an elastic beam simply supported at left and clamped at right by sliding clamps. Because the nonlinear term concerns with the bending moment,main results is useful for the stability analysis of the beam.

关 键 词：奇异常微分方程 边值问题 正解 存在性 

分 类 号：O175.8[理学—数学]