In this paper, a third-order ordinary differential equation coupled to three-point boundary conditions is considered. The related Green’s function changes its sign on the square of definition. Despite this, we are able to deduce the existence of positive and increasing functions on the whole interval of definition, which are convex in a given subinterval. The nonlinear considered problem consists on the product of a positive real parameter, a nonnegative function that depends on the spatial variable and a time dependent function, with negative sign on the first part of the interval and positive on the second one. The results hold by means of fixed point theorems on suitable cones.

中文翻译：

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具有三点边界条件的三阶微分方程

本文考虑了与三点边界条件耦合的三阶常微分方程。相关的格林函数在定义的平方上更改其符号。尽管如此，我们仍可以推断出在整个定义区间上正函数和递增函数的存在，它们在给定的子区间中是凸的。所考虑的非线性问题由正实参量，取决于空间变量的非负函数和与时间有关的函数的乘积组成，时间间隔的第一部分为负号，第二部分为正值。通过固定点定理将结果保存在适当的圆锥上。