节点文献
一类三阶常微分方程非线性三点边值问题解的存在性(英文)
Existence of Solutions of a Nonlinear Three-Point Boundary Value Problem for Third-Order Ordinary Differential Equations
【摘要】 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.
【Abstract】 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.
【Key words】 Existence of solutions； three-point boundary value problems； upper and lower solutions method； Leray-Schauder degree theory；
- 【文献出处】 数学研究与评论 ,Journal of Mathematical Research and Exposition , 编辑部邮箱 ,2009年01期
- 【分类号】O175.8
- 【被引频次】11
- 【下载频次】159