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Infinitely many solutions of a symmetric semilinear elliptic equation on an unbounded domain

Maad, Sara LU (2003) In Arkiv for Matematik 41(1). p.105-114
Abstract
We study a semilinear elliptic equation of the form
−Δu+u=f(x,u),u∈H^1_0(Ω),
wheref is continuous, odd in u and satisfies some (subcritical) growth conditions. The domain Ω⊂R^N is supposed to be an unbounded domain (N≥3). We introduce a class of domains, called strongly asymptotically contractive, and show that for such domains Ω, the equation has infinitely many solutions.
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author
publishing date
type
Contribution to journal
publication status
published
subject
in
Arkiv for Matematik
volume
41
issue
1
pages
10 pages
publisher
Springer
external identifiers
  • scopus:29144447864
ISSN
0004-2080
DOI
10.1007/BF02384570
language
English
LU publication?
no
id
3e05e204-f95f-42b0-a289-472436e303c6
date added to LUP
2017-02-08 13:23:25
date last changed
2017-02-15 13:30:33
@article{3e05e204-f95f-42b0-a289-472436e303c6,
  abstract     = {We study a semilinear elliptic equation of the form<br/>−Δu+u=f(x,u),u∈H^1_0(Ω),<br/>wheref is continuous, odd in u and satisfies some (subcritical) growth conditions. The domain Ω⊂R^N is supposed to be an unbounded domain (N≥3). We introduce a class of domains, called strongly asymptotically contractive, and show that for such domains Ω, the equation has infinitely many solutions.},
  author       = {Maad, Sara},
  issn         = {0004-2080},
  language     = {eng},
  number       = {1},
  pages        = {105--114},
  publisher    = {Springer},
  series       = {Arkiv for Matematik},
  title        = {Infinitely many solutions of a symmetric semilinear elliptic equation on an unbounded domain},
  url          = {http://dx.doi.org/10.1007/BF02384570},
  volume       = {41},
  year         = {2003},
}