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UNIQUENESS AND NONEXISTENCE OF POSITIVE SOLUTIONS TO SEMIPOSITONE PROBLEMS
E. NORMAN DANCER, JUNPING SHI
Journal:

Bulletin of the London Mathematical Society / Volume 38 / Issue 6 / December 2006

Published online by Cambridge University Press:

19 December 2006, pp. 1033-1044

Print publication:

December 2006
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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.

ON THE EXISTENCE OF EXTREMALS FOR THE SOBOLEV TRACE EMBEDDING THEOREM WITH CRITICAL EXPONENT
JULIÁN FERNÁNDEZ BONDER, JULIO D. ROSSI
Journal:

Bulletin of the London Mathematical Society / Volume 37 / Issue 1 / January 2005

Published online by Cambridge University Press:

08 February 2005, pp. 119-125

Print publication:

January 2005
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In this paper, the existence problem is studied for extremals of the Sobolev trace inequality $W^{1,p}(\Omega)\to L^{p_*}(\partial\Omega)$, where $\Omega$ is a bounded smooth domain in $\RR^N$, $p_*=p(N-1)/(N-p)$ is the critical Sobolev exponent, and $1<p<N$.