中文摘要：

讨论了一类半无穷区间上二阶非线性常微分方程三点边值问题的可解性．通过建立无界上下解理论，利用上下解，Schauder不动点定理和不等式技巧，给出了这类问题解存在的充分条件．该文的创新之一就是建立了多点边值问题的无界上下解理论．

英文摘要：

This paper discusses the existence of unbounded solutions to three-point boundary value problems of second order nonlinear differential equations on the half line. By establishing the unbounded upper and lower solutions theory, using the upper and lower solutions, the Schauder fixed point theorem and inequality technique, sufficient conditions are obtained to guarantee the existence of solution. One interesting point is that the unbounded upper and lower solutions theory is established for three-point boundary value problem.