Subfunctions for second order ordinary differential equations

Thompson, H. B. (2000) Subfunctions for second order ordinary differential equations. Applicable Analysis, 74 1-2: 27-43. doi:10.1080/00036810008840801

Author Thompson, H. B.
Title Subfunctions for second order ordinary differential equations
Journal name Applicable Analysis   Check publisher's open access policy
ISSN 0003-6811
Publication date 2000-02-01
Sub-type Article (original research)
DOI 10.1080/00036810008840801
Volume 74
Issue 1-2
Start page 27
End page 43
Total pages 17
Editor R. P. Gilbert
Place of publication New York, NY, U.S.A.
Publisher Taylor & Francis
Collection year 2000
Language eng
Subject C1
230107 Differential, Difference and Integral Equations
780101 Mathematical sciences
Formatted abstract
Lloyd Jackson adapted the Perron process to the study of boundary value problems for equations of the form y″ = f(x, y, y′). He introduced subfunctions, the analogue of subharmonic functions and, under strong assumptions on f, established smoothness results for the pointwise supremum z of a suitable family of subfunctions and showed z is a solution. Assuming only continuity of f, we establish sharp smoothness properties for z and show it is almost a solution thus improving on our earlier results in this direction. We apply these results to establish some existence theorems for two point boundary value problems. As a second application we describe the relationship between Jackson's subfunctions and the various subfunctions, including F-subfunctions, introduced independently by K. Ako.
 © 2000 OPA (Overseas Publishers Association) N.V.
Q-Index Code C1

Document type: Journal Article
Sub-type: Article (original research)
Collection: School of Physical Sciences Publications
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Created: Tue, 10 Jun 2008, 22:24:33 EST