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

Sara Maad Department of Mathematics, Uppsala University

TBD mathscidoc:1701.332996

Arkiv for Matematik, 41, (1), 105-114, 2001.7
We study a semilinear elliptic equation of the form $$ - \Delta u + u = f(x,u), u \in H_0^1 (\Omega ),$$ where$f$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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@inproceedings{sara2001infinitely,
  title={Infinitely many solutions of a symmetric semilinear elliptic equation on an unbounded domain},
  author={Sara Maad},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203606321809805},
  booktitle={Arkiv for Matematik},
  volume={41},
  number={1},
  pages={105-114},
  year={2001},
}
Sara Maad. Infinitely many solutions of a symmetric semilinear elliptic equation on an unbounded domain. 2001. Vol. 41. In Arkiv for Matematik. pp.105-114. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203606321809805.
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