二阶两点边值问题的多解存在性

Existence of Multiple Solutions to a Second-Order Two-Point Boundary Value Problem

中文关键词:  边值问题  Leray-Schauder度  多解  上下解.

英文关键词:boundary value problems  Leray-Schauder degree  multiple solutions  upper and lower solutions.

中文摘要:

      本文讨论一类二阶两点边值问题$x^{\prime\prime}(t)+f(t,x(t),x^{\prime}(t))=0, t\in (0, 1)$, $a x(0)-b x^\prime(0)=0, ~~c x(1)+d x^\prime(1)=0$,~~其中 $f:[0,1]\times R^2\longrightarrow R$ 是连续的, $ a>0,b\ge 0,c>0,d\ge 0$. 通过运用上下解方法和 Leray-Schauder 度理论,得到了三个解的存在性结果.

英文摘要:

      In this paper, we consider a class of second-order two-point boundary value problem~~ $x^{\prime\prime}(t)+f(t,x(t),x^{\prime}(t))=0,~~ t\in (0, 1)$, $a x(0)-b x^\prime(0)=0, ~~c x(1)+d x^\prime(1)=0$,~~ where $f:[0,1]\times R^2\longrightarrow R$ is continuous, $ a>0,b\ge 0,c>0$, and $d\ge 0$. By using upper and lower solutions method and Schauder degree theory, we obtain the existence of three solutions.