三阶非线性微分方程正解的存在性

Existence of Positive Solutions For Third-Order Nonlinear Differential Equations

证明了非线性三阶微分方程ｕ＂＇十ａ（ｔ）ｆ（ｕ）＝０满足下列条件之一：的两点边值问题正解的存在性，只要ｆ（ｕ）于两个端点ｕ＝０和ｕ＝十∞处或者是超线性的或者是次线性的．

The existence of positive solutions for the third-order nonlinear differential equationu''+a(t)f(u)=0which satisfies one of the following two-point boundary value u(0)=0,u' (0)=0,u(1)=0;u(0)=0,u' (0)=0,u' (1)=0; prolerm u(0)=0,u' (0)=0,u'(1)=0;u(0)=0,u'(0)=0,u(1)=0;u(0)=0,u'(0)=0,u' (1)=0;u' (0)=0,u'(0)=0,u (1)=0 is proved if f is either suplinear or sublinear at two endpoint u=0 and u=+∞.