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Property of positive solutions and its applications for Sturm–Liouville singular boundary value problems

✍ Scribed by Zengqin Zhao

Publisher
Elsevier Science
Year
2008
Tongue
English
Weight
384 KB
Volume
69
Category
Article
ISSN
0362-546X

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✦ Synopsis

This paper is concerned with the property of the positive solutions for Sturm-Liouville singular boundary value problems with the linear conditions. We obtain a relation between the solutions and Green's function. It implies a necessary condition for the C 1 [0, 1] positive solutions. We apply the result to conclude that the given equation has no C 1 [0, 1] positive solutions.

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In this paper, by using the fixed point index method, we establish the existence of at least one or at least two positive solutions for the third-order Sturm-Liouville boundary value problem with p-Laplacian where φ p (s) = |s| p-2 s, p > 1. As an application, an example is given to demonstrate the