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

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dc.contributor.advisor Henderson, Johnny.
dc.contributor.author Gray, Michael Jeffery.
dc.contributor.other Baylor University. Dept. of Mathematics. en
dc.date.copyright 2006-05-13
dc.identifier.uri http://hdl.handle.net/2104/4185
dc.description.abstract 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. en
dc.rights Baylor 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. en
dc.subject Boundary value problems -- Research. en
dc.subject Differential equations -- Research. en
dc.title Uniqueness implies uniqueness and existence for nonlocal boundary value problems for third order ordinary differential equations. en
dc.type Thesis en
dc.description.degree Ph.D. en
dc.rights.accessrights Worldwide access. en
dc.rights.accessrights Access changed 5/24/11.
dc.contributor.department Mathematics. en


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