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Positive solutions to a second order three-point boundary value problem

✍ Scribed by Zhongxin Zhang; Junyu Wang

Publisher: Elsevier Science
Year: 2003
Tongue: English
Weight: 118 KB
Volume: 285
Category: Article
ISSN: 0022-247X
DOI: 10.1016/s0022-247x(03)00396-2

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✦ Synopsis

The existence, nonexistence, and multiplicity of nonnegative solutions are established for the three-point boundary value problem

where β ∈ (0, 1), α ∈ (0, 1/β), and λ is a nonnegative parameter, under appropriate hypotheses. The key idea is that the problem of finding a nonnegative solution is transformed into the problem of finding a fixed point of a completely continuous operator. The arguments involve the Schauder fixed point, the method of upper and lower solutions for three-point boundary value problems and the Leray-Schauder degree theory.

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