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UNIQUENESS AND NONEXISTENCE OF POSITIVE SOLUTIONS TO SEMIPOSITONE PROBLEMS

Published online by Cambridge University Press:  19 December 2006

E. NORMAN DANCER  and
JUNPING SHI
E. NORMAN DANCER
Affiliation:
School of Mathematics and Statistics, University of Sydney, Sydney, NSW2006, [email protected]
JUNPING SHI
Affiliation:
Department of Mathematics, College of William and Mary, Williamsburg, VA 23187, USA and School of Mathematics, Harbin Normal University, Harbin, Heilongjiang 150080, [email protected]
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Abstract

We consider the uniqueness of the positive solution to a semilinear elliptic equation with Dirichlet boundary condition and the nonlinearity satisfying $f(0)<0$ and having asymptotic sublinear growth rate. A similar idea is also applied to the nonexistence of a positive solution to a superlinear problem.

Keywords

35J65 (primary)35B40 (secondary)
Type
Papers
Information
Bulletin of the London Mathematical Society , Volume 38 , Issue 6 , December 2006 , pp. 1033 - 1044
Copyright
The London Mathematical Society 2006

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