UNIQUENESS FOR SINGULAR SEMILINEAR ELLIPTIC BOUNDARY VALUE PROBLEMS

We prove uniqueness of positive solutions for the boundary value problems \[ \{\begin{array}{ll} -\Delta u=\lambda f(u)\ \ &\text{in}\Omega, \ \ \ \ \ u=0 &\text{on \partial \Omega, \] where Ω is a bounded domain in ℝn with smooth boundary ∂Ω, λ is a positive parameter and f:(0,∞) → (0,∞) is...

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Bibliographic Details
Published inGlasgow mathematical journal Vol. 55; no. 2; pp. 399 - 409
Main Authors HAI, D. D., SMITH, R. C.
Format Journal Article
LanguageEnglish
Published Cambridge, UK Cambridge University Press 01.05.2013
Subjects
Boundaries
Boundary value problems
Mathematical analysis
Uniqueness
35J75
35J92
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Summary:We prove uniqueness of positive solutions for the boundary value problems \[ \{\begin{array}{ll} -\Delta u=\lambda f(u)\ \ &\text{in}\Omega, \ \ \ \ \ u=0 &\text{on \partial \Omega, \] where Ω is a bounded domain in ℝn with smooth boundary ∂Ω, λ is a positive parameter and f:(0,∞) → (0,∞) is sublinear at ∞ and is allowed to be singular at 0.
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ISSN:0017-0895
1469-509X
DOI:10.1017/S001708951200064X