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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

Information

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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