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A uniqueness result for a singular nonlinear eigenvalue problem

Published online by Cambridge University Press:  17 July 2013

Alfonso Castro
Department of Mathematics, Harvey Mudd College, Claremont, CA 91711, USA (
Eunkyung Ko
Department of Mathematics and Statistics, Mississippi State University, Mississippi State, MS 39762, USA (
R. Shivaji
Department of Mathematics and Statistics, University of North Carolina at Greensboro, Greensboro, NC 27412, USA (


We consider the positive solutions to singular boundary-value problems of the form where λ > 0, β ∈ (0,1) and Ω is a bounded domain in ℝN, N ≥ 1, with smooth boundary ∂Ω. Here, we assume that f: [0, ∞) → (0, ∞) is a C1 non-decreasing function and f(s)/sβ is decreasing for s large. We establish the uniqueness of the positive solution when λ is large.

Research Article
Copyright © Royal Society of Edinburgh 2013 

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