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Comparison of smallest eigenvalues and extremal points for third and fourth order three point boundary value problems.

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dc.contributor.advisor Henderson, Johnny.
dc.contributor.author Neugebauer, Jeffrey T.
dc.date.copyright 2011-08
dc.identifier.uri http://hdl.handle.net/2104/8235
dc.description.abstract The theory of u₀-positive operators with respect to a cone in a Banach space is applied to the linear differential equations u⁽⁴⁾ + λ₁p(x)u = 0 and u⁽⁴⁾ + λ₂q(x)u = 0, 0 ≤ x ≤ 1, with each satisfying the boundary conditions u(0) = u′(r) = u″(r) = u‴(1) = 0, 0 < r < 1. The existence of smallest positive eigenvalues is established, and a comparison theorem for smallest positive eigenvalues is obtained. These results are then extended to the nth order problem using two different methods. One method involves finding the Green's function for –u⁽ⁿ⁾ = 0 satisfying the higher order boundary conditions, and the other involves making a substitution that allows us to work with a variation of the fourth order problem. Extremal points via Krein-Rutman theory are then found. Analogous results are then obtained for the eigenvalue problems u‴ + λ₁p(x)u = 0 and u‴ + λ₂q(x)u = 0, with each satisfying u(0) = u′(r) = u″(1) = 0, 0 < 1/2 < r < 1. en_US
dc.publisher 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_US
dc.subject Differential equations. en_US
dc.subject Eigenvalue problems. en_US
dc.subject Extremal points. en_US
dc.title Comparison of smallest eigenvalues and extremal points for third and fourth order three point boundary value problems. en_US
dc.type Thesis en_US
dc.description.degree Ph.D. en_US
dc.rights.accessrights Worldwide access. en_US
dc.rights.accessrights Access changed 6/27/13.
dc.contributor.department Mathematics.
dc.contributor.schools Baylor University. Dept. of Mathematics. en_US


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