Differentiability properties of subfunctions for second order ordinary differential equations

Thompson H.B. (1989) Differentiability properties of subfunctions for second order ordinary differential equations. Pacific Journal of Mathematics, 140 1: 181-207.

Author Thompson H.B.
Title Differentiability properties of subfunctions for second order ordinary differential equations
Journal name Pacific Journal of Mathematics   Check publisher's open access policy
ISSN 0030-8730
Publication date 1989
Sub-type Article (original research)
Volume 140
Issue 1
Start page 181
End page 207
Total pages 27
Subject 2600 Mathematics
Abstract We obtain sharp differentiability results for subfunctions for second order ordinary differential equations y’' = f(x, y, y’) on [a, b]. In the process we show that a subfunction satisfies a second order differential inequality similar to that satisfied by a lower solution. We show that a subfunction can be used in maximum principle arguments in the same way one uses a lower solution. As an application of these results we give necessary and sufficient conditions on a function in order that there is a differential equation for which it is a subfunction. We use our results together with the Perron method to improve on some existence results for two point boundary value problems obtained by Jackson, using Perron’s method.
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Unknown

Document type: Journal Article
Sub-type: Article (original research)
Collection: Scopus Import
 
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Created: Tue, 05 Jul 2016, 05:55:38 EST by System User