Triple Solutions for Second-order Three-point Boundary Value Problems
We establish the existence of at least three positive solutions to the second-order three-point boundary value problem, u″ + f(t, u) = 0, u(0) = 0, αu(η) = u(1), where η: 0 lt; η < 1, 0 < α < 1/η, andf: [0, 1] × [0, ∞) → [0, ∞) is continuous. We accomplish this by making growth assumptions on f which can apply to many more cases than the sublinear and superlinear ones discussed in recent works.
X. He and W. Ge, "Triple Solutions for Second-order Three-point Boundary Value Problems," Journal of Mathematical Analysis and Applications, Elsevier, Jan 2002.
The definitive version is available at https://doi.org/10.1006/jmaa.2001.7824
Mathematics and Statistics
Keywords and Phrases
Three-point boundary value problem; multiple solutions; fixed points; cone
International Standard Serial Number (ISSN)
Article - Journal
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