四阶奇异m点边值问题的正解

The Existence of Positive Solutions for Fourth Order Singular m-point Boundary Value Problems

利用上下解方法,不动点定理研究了四阶奇异m点边值问题正解存在性.通过构造上下解和比较定理给出了C^2[0,1]和C^3[0,1]正解存在的充分条件.非线性项f(t,u)在t=0,t=1和u=0处奇异,关于u减而且仅仅具有某些可积性.

In this paper,using the methods of lower and upper solution,and the fixed point theorem,the existence of positive solutions for a class of fourth order singular m-point boundary value problems is investigated.A sufficient condition for the existence of C^2[0,1]as well as C^3[0,1]positive solutions is given by constructing lower and upper solutions and with the comparison theorem.The nonlinearity f（t,u）may be singular at t=0,t=1and u=0,and f（t,u）is decreasing on u and only have some integrality.