一类三阶常微分方程非线性三点边值问题解的存在性

Existence of Solutions of a Nonlinear Three-Point Boundary Value Problem for Third-Order Ordinary Differential Equations

中文关键词:  解的存在性  非线性三点边值问题  上下解法  Leray-Schauder度理论.

英文关键词:Existence of solutions  three-point boundary value problems  upper and lower solutions method  Leray-Schauder degree theory.

中文摘要:

      结合上下解方法及Leray-Schauder度理论, 通过定义适当的上下解及Nagumo条件和引入适当的辅助边值问题, 得到了如下三阶常微分方程非线性三点边值问题解的存在性.\begin{eqnarray}\left\{ \begin{array}{l} y'''(t)=f(t,y(t),y'(t),y''(t))\\ g(y(a),y

英文摘要:

      In this paper, existence of solutions of third-order differential equation $$y'''(t)=f(t,y(t),y'(t),y''(t))$$ with nonlinear three-point boundary condition $$\left\{ \begin{array}{l} g(y(a),y'(a),y''(a))=0,\\h(y(b),y'(b))=0,\\I(y(c),y'(c),y''(c))=0\end{array}\right.$$is obtained by embedding Leray-Schauder degree theory in upper and lower solutions method, where $a, b, c\in R, a