A functional approach to positive solutions of boundary value problems.

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dc.contributor.advisor Henderson, Johnny. Ehrke, John E.
dc.contributor.other Baylor University. Dept. of Mathematics. en 2007-05
dc.description.abstract 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. 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 for inquiries about permission. en
dc.subject Boundary value problems. en
dc.subject Fixed point theory. en
dc.subject Functionals. en
dc.title A functional approach to positive solutions of boundary value problems. en
dc.type Thesis en Ph.D. en
dc.rights.accessrights Worldwide access en
dc.contributor.department Mathematics. en

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