Change search
ReferencesLink to record
Permanent link

Direct link
A Supercritical Elliptic Problem in a Cylindrical Shell
Stockholm University, Faculty of Science, Department of Mathematics.
2014 (English)In: Analysis and Topology in Nonlinear Differential Equations: A Tribute to Bernhard Ruf on the Occasion of his 60th Birthday / [ed] de Figueiredo et al, Basel: Birkhäuser , 2014, 233-242 p.Chapter in book (Refereed)
Abstract [en]

We consider the problem \[-\Delta u=\left\vert u\right\vert ^{p-2}u\text{ \ in }\Omega,\quad u=0\text{\ on }\partial\Omega,\]where $\Omega:=\{(y,z)\in\mathbb{R}^{m+1}\times\mathbb{R}^{N-m-1}%:0<a<\left\vert y\right\vert <b<\infty\}$, $0\leq m\leq N-1$ and $N\geq2.$ Let$2_{N,m}^{\ast}:=2(N-m)/(N-m-2)$ if $m<N-2$ and $2_{N,m}^{\ast}:=\infty$ if$m=N-2$ or $N-1.$ We show that $2_{N,m}^{\ast}$ is the true critical exponent forthis problem, and that there exist nontrivial solutions if $2<p<2_{N,m}^{\ast}$ butthere are no such solutions if $p\geq2_{N,m}^{\ast}$.

Place, publisher, year, edition, pages
Basel: Birkhäuser , 2014. 233-242 p.
, Progress in Nonlinear Differential Equations and Their Applications, 85
Keyword [en]
Nonlinear elliptic equation, supercritical nonlinearity, unbounded domain
National Category
Mathematical Analysis
Research subject
URN: urn:nbn:se:su:diva-102354ISBN: 978-3-319-04213-8OAI: diva2:709774
Swedish Research Council
Available from: 2014-04-03 Created: 2014-04-03 Last updated: 2014-04-08Bibliographically approved

Open Access in DiVA

No full text

Other links

FörlagssidaRecent publications

Search in DiVA

By author/editor
Szulkin, Andrzej
By organisation
Department of Mathematics
Mathematical Analysis

Search outside of DiVA

GoogleGoogle Scholar
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

Total: 24 hits
ReferencesLink to record
Permanent link

Direct link