Uniqueness of positive radial solutions for semilinear elliptic equations on annular domains. (English) Zbl 0996.34018
The authors study the semilinear Dirichlet boundary value problem
\[
\bigtriangleup u+f(u)=0 \text{ in} \;\Omega,\quad u=0 \text{ on} \;\partial \Omega, \tag{1}
\]
where \(\Omega\) is an annular domain in \(\mathbb{R}^n\), \(n\geq 3\). They are interested in the existence of a unique positive radial solution to (1), and they prove sufficient conditions for existence and uniqueness. Particularly, they discuss the case \(f(u)=-u+u^p\), \(3\leq n \leq 5\) and \(1<p\leq \text{ min}(4/(n-2), n/(n-2))\). In this way, they get a uniqueness result that extends Coffman’s one which was reached for \(n=3\) and \(1<p\leq 3\).
Reviewer: Irena Rachůnková (Olomouc)
MSC:
| 34B18 | Positive solutions to nonlinear boundary value problems for ordinary differential equations |
Keywords:
uniqueness; existence; positive radial solutions; Dirichlet boundary conditions; annular domainReferences:
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