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UNIQUENESS FOR SINGULAR SEMILINEAR ELLIPTIC BOUNDARY VALUE PROBLEMS

Published online by Cambridge University Press:  25 February 2013

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

Keywords

35J7535J92
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 55 , Issue 2 , May 2013 , pp. 399 - 409
Copyright
Copyright © Glasgow Mathematical Journal Trust 2013

References

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