Theoretical and Numerical Aspects of a Third-order Three-point Nonhomogeneous Boundary Value Problem

ABSTRACT In this paper we are considering a third-order three-point equation with nonhomogeneous conditions in the boundary. Using Krasnoselskii’s Theorem and Leray-Schauder Alternative we provide existence results of positive solutions for this problem. Nontrivials examples are given and a numerical method is introduced.

摘要 本文针对一类带有非齐次边界条件的三阶三点方程展开研究。借助克拉索夫斯基定理（Krasnoselskii’s Theorem）与勒雷-绍德尔抉择（Leray-Schauder Alternative），本文给出了该问题正解的存在性结果。此外，本文提供了非平凡示例，并引入了一种数值方法。