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Multiple positive solutions to singular boundary value problems for superlinear higher-order ODEs

✍ Scribed by Daqing Jiang

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 426 KB
Volume: 40
Category: Article
ISSN: 0898-1221
DOI: 10.1016/s0898-1221(00)00158-9

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✦ Synopsis

For 1 < k < n-1, we study the existence of multiple positive solutions to the singular (k, n -k) conjugate boundary value problem

We show that there are at least two positive solutions if f(t, y) is superlinear at c~ and singular at u = 0, t = 0, and t = 1. The arguments involve only positivity properties of Green's function and a fixed-point theorem in cones. Moreover, the explicit formula of Green's function can be found in this paper. (~) 2000 Elsevier Science Ltd. All rights reserved.

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