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

Maad, Sara LU (2003) In Arkiv för 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.
Please use this url to cite or link to this publication:
author
publishing date
type
Contribution to journal
publication status
published
subject
in
Arkiv för 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
2025-04-04 14:10:20
@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 för Matematik}},
  title        = {{Infinitely many solutions of a symmetric semilinear elliptic equation on an unbounded domain}},
  url          = {{http://dx.doi.org/10.1007/BF02384570}},
  doi          = {{10.1007/BF02384570}},
  volume       = {{41}},
  year         = {{2003}},
}