A functional approach to positive solutions of boundary value problems.

We apply a well-known fixed point theorem to guarantee the existence of a positive solution and bounds for solutions for second, third, fourth, and nth order families of boundary value problems. We begin by characterizing second order problems having left and right focal boundary conditions. Via an appropriate substitution, associated third, fourth, and nth order problems are resolved. Our main result centers on the nth order equation y(n) + f(y(t)) = 0, t [is an element of] [0, 1], (1) having boundary conditions, y(ri−1)(0) = 0, 1 < i < k, (2) y(sj−1)(1) = 0, 1 < j < n − k, (3) where {s1, · · · , sn−k} and {r1, · · · , rk} form a partition of {1, · · · , n} such that r1 < · · · < rk, s1 < · · · < sn−k, and {rk−1 · · · rk} [is not equal to] {n − 1, n} and {sn−k−1, sn−k} [is not equal to] {n − 1, n}. Under these assumptions we show that the differential equation (1) with boundary conditions (2) and (3) has a positive solution for all n [is greater than or equal to] 2.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Doctoral

Grantor

Baylor University.

Year dc:date.issued

2007

Author dc:creator

• Ehrke, John E.

Advisor dc:contributor.advisor

• Henderson, Johnny.

• Boundary value problems.
• Fixed point theory.
• Functionals.

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/2104/5026

OAI identifier oai:identifier

oai:baylor-ir.tdl.org:2104/5026