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