Henderson, Johnny.Gray, Michael Jeffery.Baylor University. Dept. of Mathematics.2006-07-292006-07-292006-05-132006-07-29http://hdl.handle.net/2104/4185Includes bibliographical references (p. 53-56).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 \[y(x_1)=y_1,\ y(x_2)=y_2,\] \[y(x_m)-\sum_{i=3}^{m-1} y(x_{i})=y_3,\] $a<x_1<x_2<\cdots<x_m<b$, and $y_1,y_2,y_3\in\mathbb{R}$, are unique when they exist. It is proved that, for all $3\leq k \leq m$, solutions of nonlocal boundary value problems satisfying \[y(x_1)=y_1,\ y(x_2)=y_2,\] \[y(x_k)-\sum_{i=3}^{k-1} y(x_{i})=y_3,\] $a<x_1<x_2<\cdots<x_k<b$, and $y_1,y_2,y_3\in\mathbb{R}$, are unique when they exist. It is then shown that solutions do indeed exist.iv, 56 p.299906 bytes109885 bytesapplication/pdfapplication/pdfen-USBaylor University theses 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 librarywebmaster@baylor.edu for inquiries about permission.Boundary value problems -- Research.Differential equations -- Research.ThesisWorldwide access.Access changed 5/24/11.