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

作　　者：SHEN Jian He ZHOU Zhe Yan YU Zan Pin 

机构地区：[1]School of Mathematics and Computer Science, Fujian Normal University, Fujian 350007, China [2]Department of Applied Mechanics and Engineering, Sun Yat-Sen University, Guangdong 510275, China

出　　处：《Journal of Mathematical Research and Exposition》2009年第1期57-64,共8页数学研究与评论（英文版）

基　　金：Foundation item： the Natural Science Foundation of Fujian Province （No. S0650010）.

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{g（y（a）,y′（a）,y″（a））=0, h（y（b）,y′（b））=0, I（y（c）,y′（c）,y″（c））=0is obtained by embedding Leray-Schauder degree theory in upper and lower solutions method,where a, b, c∈ R,a〈 b〈 c; f ： [a,c]×R^3→R,g：R^3→R,h：R^2→R and I：R^3→R are continuous functions. The existence result is obtained by defining the suitable upper and lower solutions and introducing an appropriate auxiliary boundary value problem. As an application, an example with an explicit solution is given to demonstrate the validity of the results in this paper.In this paper,existence of solutions of third-order differential equation ■with nonlinear three-point boundary condition ■is obtained by embedding Leray-Schauder degree theory in upper and lower solutions method,where a,b,c ∈ R,a < b < c;f :[a,c]×R3 → R,g :R3 → R,h :R2 → R and I :R3 → R are continuous functions.The existence result is obtained by defining the suitable upper and lower solutions and introducing an appropriate auxiliary boundary value problem.As an application,an example with an explicit solution is given to demonstrate the validity of the results in this paper.

关 键 词：Existence of solutions three-point boundary value problems upper and lowe solutions method Leray-Schauder degree theory. 

分 类 号：O175.1[理学—数学]