Uniqueness implies uniqueness and existence for nonlocal boundary value problems for third order ordinary differential equations.

For the third order ordinary differential equation, $y'''=f(x,y,y',y'')$, it is assumed that, for some $m\geq 4$, solutions of nonlocal boundary value problems satisfying \[y(x_1)=y_1,\ y(x_2)=y_2,\] \[y(x_m)-\sum_{i=3}^{m-1} y(x_{i})=y_3,\] a<x₁<x₂<\cdots<x_m<b, and y₁,y₂,y₃\in\mathbb{R}, are unique when they exist. It is proved that, for all $3\leq k \leq m$, solutions of nonlocal boundary value problems satisfying \[y(x_1)=y_1,\ y(x_2)=y_2,\] \[y(x_k)-\sum_{i=3}^{k-1} y(x_{i})=y_3,\] a<x₁<x₂<\cdots<x_k<b, and y₁,y₂,y₃\in\mathbb{R}, are unique when they exist. It is then shown that solutions do indeed exist.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Doctoral

Grantor

Baylor University.

Year dc:date.issued

2006

Author dc:creator

• Gray, Michael Jeffery.

Advisor dc:contributor.advisor

• Henderson, Johnny.

• Boundary value problems -- Research.
• Differential equations -- Research.

Statement dc:rights

• Baylor University works are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. Contact libraryquestions@baylor.edu for inquiries about permission.

Language dc:language.iso

en

Handle dc:identifier.uri

https://hdl.handle.net/2104/4185

OAI identifier oai:identifier

oai:baylor-ir.tdl.org:2104/4185