Existence of Solutions of a Nonlinear Three-Point Boundary Value Problem for Third-Order Ordinary Differential Equations
Received:November 05, 2006  Revised:April 16, 2007
Key Word: Existence of solutions   three-point boundary value problems   upper and lower solutions method   Leray-Schauder degree theory.
Fund ProjectL:the Natural Science Foundation of Fujian Province (No.S0650010).
 Author Name Affiliation SHEN Jian He School of Mathematics and Computer Science, Fujian Normal University, Fujian 350007, China Department of Applied Mechanics and Engineering, Sun Yat-Sen University, Guangdong 510275, China ZHOU Zhe Yan School of Mathematics and Computer Science, Fujian Normal University, Fujian 350007, China YU Zan Ping School of Mathematics and Computer Science, Fujian Normal University, Fujian 350007, China
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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