考察了非线性三阶三点广义右聚焦边值问题$$\begin{array}{c}{u}^{‴}(t)=f(t,u(t)),0<t<1,\text{q}u(0)=u^{\prime }(\eta )=0,\text{q}\gamma u(1)+{\text{deltau}}^{″}(1)=0\end{array}$$的正解存在性与多解性, 其中$\frac{1}{2}<\eta <1$并且$f(t,u)$可以在$t=0,t=1$及$u=0$处奇异. 通过引入两个非线性项在燕尾形区域上的高度函数,并且考察这些高度函数的积分来估计解的先验界. 根据锥拉伸锥压缩型的Guo-Krasnoselskii不动点定理获得了某些新的结论.

The existence and multiplicity of positive solutions are considered for the nonlinear third-order three-point generalized right focal boundary value problems
u′′′(t) = f(t, u(t)), 0 < t < 1, u(0) = u′() = 0,  u(0) + u′′(1) = 0, where 1 2 <  < 1 and the olinear term f(t, u) may be singular at t = 0, t = 1 and u = 0. By introducing two height functions of the nonlinear term on some swallow- tailed regions and considering integrations of the height functions, the a priori bound
of solution is estimated. According to the Guo-Krasnoselskii fixed point theorem of cone expansion-compression type, several new results are obtained.