Doctoral Dissertations

Abstract

"Consider the boundary value problem y = 0, y(a) = 0, y(b) = O. The Green's function G(x,s) for this problem is negative for all (x,s) in (a,b) x (a,b). More generally, define the operator L by (formula presented).

If L is disconjugate on [a,b], then the Green's function for the problem

Ly = 0,

y(i) (x.) = O, j=1, ..., k and i=0, ..., nj-1

where rnj = n and a= x1 < x2 < ... < xk = b, satisfies the inequality (formula presented)

This implies G(x,s) satisfies the condition, called Condition S, that its sign is independent of s.

We construct monotone iteration schemes whenever Condition S holds for the Green's function, to obtain existence theorems and to approximate solutions of boundary value problems of the form

Ly= f(x,y),

Ty= r,

where T represents linear boundary conditions. These results include extensions of recent work of Ju. I. Kovac, V. Seda, L. Collatz, and others.

J. Werner has obtained existence theorems of a similar nature for solutions of two-point boundary value problems for first order differential systems. We construct a Green's matrix for a multi-point problem for systems and extend some of Werner's results to this case."-- Abstract, pp. ii-iii

Advisor(s)

Grimm, L. J., -2010

Committee Member(s)

Trimble, S. Y.
Haddock, Glen
Plummer, O. R.
Keith, Harold D. (Harold Dean), 1941-

Department(s)

Mathematics and Statistics

Degree Name

Ph. D. in Mathematics

Publisher

University of Missouri--Rolla

Publication Date

Summer 1980

Pagination

v, 56 pages

Note about bibliography

Includes bibliographical references (pages 53-55)

Rights

© 1980 Paul W. Eloe, All rights reserved.

Document Type

Dissertation - Open Access

File Type

text

Language

English

Thesis Number

T 4589

Print OCLC #

7444594

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Included in

Mathematics Commons

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