一类四阶常微分方程两点边值问题正解的存在性

Existence of Positive Solutions for a Class of Fourth-order Ordinary Differential Equations of Two-point Boundary Value Problem

本文利用不动点指数理论研究具有超线性或次线性的非线性的四阶两点边值问题的正解存在性问题。文中给出了保证正解存在的参数取值范围及对应不存在正解的参数取值范围。本文主要结果推广并改进了一些已知结果。

Based on the fixed-point index theory, we investigate the existence of positive solutions to a class of boundary value problems of fourth-order ordinary differential equations with a nonlinearity which is superlinearity or sublineraity. We propose an interval of parameters to ensure the existence of positive solutions, and we find another interval of parameters corresponding to the nonexistence of positive solutions. Our main result improves and generalizes some known results.