Change search

Cite
Citation style
• apa
• ieee
• modern-language-association-8th-edition
• vancouver
• Other style
More styles
Language
• de-DE
• en-GB
• en-US
• fi-FI
• nn-NO
• nn-NB
• sv-SE
• Other locale
More languages
Output format
• html
• text
• asciidoc
• rtf
A concentration phenomenon for semilinear elliptic equations
Stockholm University, Faculty of Science, Department of Mathematics.
2013 (English)In: Archive for Rational Mechanics and Analysis, ISSN 0003-9527, E-ISSN 1432-0673, Vol. 207, no 3, p. 1075-1089Article in journal (Refereed) Published
##### Abstract [en]

For a domain $\Omega\subset\dR^N$ we consider the equation $-\Delta u + V(x)u = Q_n(x)\abs{u}^{p-2}u$ with zero Dirichlet boundary conditions and $p\in(2,2^*)$. Here $V\ge 0$ and $Q_n$ are bounded functions that are positive in a region contained in $\Omega$ and negative outside, and such that the sets $\{Q_n>0\}$ shrink to a point $x_0\in\Omega$ as $n\to\infty$. We show that if $u_n$ is a nontrivial solution corresponding to $Q_n$, then the sequence $(u_n)$ concentrates at $x_0$ with respect to the $H^1$ and certain $L^q$-norms. We also show that if the sets $\{Q_n>0\}$ shrink to two points and $u_n$ are ground state solutions, then they concentrate at one of these points.

##### Place, publisher, year, edition, pages
2013. Vol. 207, no 3, p. 1075-1089
##### Keywords [en]
Concentration, semilinear elliptic equation
Mathematics
Mathematics
##### Identifiers
ISI: 000314026900012OAI: oai:DiVA.org:su-83444DiVA, id: diva2:575786
##### Funder
Swedish Research CouncilAvailable from: 2012-12-11 Created: 2012-12-11 Last updated: 2017-12-07Bibliographically approved

#### Open Access in DiVA

No full text in DiVA

Publisher's full text

#### Search in DiVA

Szulkin, Andrzej
##### By organisation
Department of Mathematics
##### In the same journal
Archive for Rational Mechanics and Analysis
Mathematics

doi
urn-nbn

#### Altmetric score

doi
urn-nbn
Total: 336 hits

Cite
Citation style
• apa
• ieee
• modern-language-association-8th-edition
• vancouver
• Other style
More styles
Language
• de-DE
• en-GB
• en-US
• fi-FI
• nn-NO
• nn-NB
• sv-SE
• Other locale
More languages
Output format
• html
• text
• asciidoc
• rtf