Differential and Integral Equations

On the uniqueness of solutions for a semilinear elliptic problem in convex domains

Angela Pistoia

Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

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.

Article information

Source
Differential Integral Equations Volume 17, Number 11-12 (2004), 1201-1212.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356060241

Mathematical Reviews number (MathSciNet)
MR2100022

Zentralblatt MATH identifier
1150.35418

Subjects
Primary: 35J60: Nonlinear elliptic equations
Secondary: 35B33: Critical exponents 35J25: Boundary value problems for second-order elliptic equations

Citation

Pistoia, Angela. On the uniqueness of solutions for a semilinear elliptic problem in convex domains. Differential Integral Equations 17 (2004), no. 11-12, 1201--1212. https://projecteuclid.org/euclid.die/1356060241.


Export citation