一类含一阶导数的二阶三点边值问题的可解性

Solvability of a class of second-order three-point boundary value problems with first derivative

利用积分方程,作者通过构造适当的Banach空间考察了一类含有一阶导数的二阶三点边值问题的解和正解的存在性.利用Leray-Schauder不动点定理,作者证明了只要非线性项在其定义域的某个有界子集上的"高度"是适当的则该类问题可以有一个解或者正解.

By using integral equation and constructing suitable Banach space, the existence of solution and positive solution is considered for a class of second-order three-point boundary value problems with first derivative, The engaged tool is the Leray-Schauder fixed point theorem. The main results show that the class of problems may have a solution or positive solution provided the ＂height＂ of nonlinear term is appropriate on a bounded set.