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UNIQUENESS FOR SINGULAR SEMILINEAR ELLIPTIC BOUNDARY VALUE PROBLEMS II

Part of: Elliptic equations and systems

Published online by Cambridge University Press:  21 July 2015

D. D. HAI  and
R. C. SMITH
D. D. HAI
Affiliation:
Department of Mathematics and Statistics, Mississippi State University, Mississippi State, MS 39762, USA e-mail: dang@math.msstate.edu, smith@math.msstate.edu
R. C. SMITH
Affiliation:
Department of Mathematics and Statistics, Mississippi State University, Mississippi State, MS 39762, USA e-mail: dang@math.msstate.edu, smith@math.msstate.edu
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Abstract

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We prove uniqueness of positive solutions for the boundary value problem

\begin{equation*} \left\{ \begin{array}{l} -\Delta u=\lambda f(u)\text{ in }\Omega , \\ \ \ \ \ \ \ \ u=0\text{ on }\partial \Omega , \end{array} \right. \end{equation*}
where Ω is a bounded domain in $\mathbb{R}$n with smooth boundary ∂ Ω, λ is a large positive parameter, f:(0,∞) → [0,∞) is nonincreasing for large t and is allowed to be singular at 0.

MSC classification

Primary: 35J75: Singular elliptic equations
Secondary: 35J92: Quasilinear elliptic equations with $p$-Laplacian
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 58 , Issue 2 , May 2016 , pp. 461 - 469
Copyright
Copyright © Glasgow Mathematical Journal Trust 2015 

References

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