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2004 On the uniqueness of solutions for a semilinear elliptic problem in convex domains
Angela Pistoia
Differential Integral Equations 17(11-12): 1201-1212 (2004).

Abstract

We exhibit a class of convex and nonsymmetric domains $\Omega$ in $\mathbb R^N,$ $N\ge4,$ such that the slightly subcritical problem $$ \begin{cases} -\Delta u=u^{{N+2\over N-2}-{\varepsilon}} & \text{ in $\Omega,$ } \\ u>0 & \text{ in $\Omega,$ } \\ u=0 & \text{ on $\partial\Omega $} \end{cases} $$ does not have any solutions blowing up at more than one point in $\Omega$ as ${\varepsilon}$ goes to zero. Moreover if $\Omega$ is a small perturbation of a convex and symmetric domain, we prove that such a problem has a unique solution provided ${\varepsilon}$ is small enough.

Citation

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Angela Pistoia. "On the uniqueness of solutions for a semilinear elliptic problem in convex domains." Differential Integral Equations 17 (11-12) 1201 - 1212, 2004.

Information

Published: 2004
First available in Project Euclid: 21 December 2012

zbMATH: 1150.35418
MathSciNet: MR2100022

Subjects:
Primary: 35J60
Secondary: 35B33 , 35J25

Rights: Copyright © 2004 Khayyam Publishing, Inc.

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Vol.17 • No. 11-12 • 2004
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