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A uniqueness result for a singular nonlinear eigenvalue problem

Published online by Cambridge University Press:  17 July 2013

Alfonso Castro ,
Eunkyung Ko  and
R. Shivaji
Alfonso Castro
Affiliation:
Department of Mathematics, Harvey Mudd College, Claremont, CA 91711, USA (castro@math.hmc.edu)
Eunkyung Ko
Affiliation:
Department of Mathematics and Statistics, Mississippi State University, Mississippi State, MS 39762, USA (ekko1115@gmail.com)
R. Shivaji
Affiliation:
Department of Mathematics and Statistics, University of North Carolina at Greensboro, Greensboro, NC 27412, USA (shivaji@uncg.edu)
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Abstract

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.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 143 , Issue 4 , August 2013 , pp. 739 - 744
Copyright
Copyright © Royal Society of Edinburgh 2013 

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