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Bound states in a locally deformed waveguide: the critical case

Pavel Exner SA Vugalter

TBD mathscidoc:1910.43040

Letters in Mathematical Physics, 39, (1), 59-68, 1997.1
We consider the Dirichlet Laplacian for astrip in \mathbb{R}^2 with one straight boundary and a width \mathbb{R}^2 , where \mathbb{R}^2 is a smooth function of acompact support with a length 2<i>b</i>. We show that in the criticalcase, \mathbb{R}^2 , the operator has nobound statesfor small \mathbb{R}^2 .On the otherhand, a weakly bound state existsprovided \mathbb{R}^2 . In thatcase, there are positive <i>c</i> <sub>1</sub>,<i>c</i> <sub>2</sub> suchthat the corresponding eigenvalue satisfies \mathbb{R}^2 for all \mathbb{R}^2 sufficiently small.
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@inproceedings{pavel1997bound,
  title={Bound states in a locally deformed waveguide: the critical case},
  author={Pavel Exner, and SA Vugalter},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020122733744528569},
  booktitle={Letters in Mathematical Physics},
  volume={39},
  number={1},
  pages={59-68},
  year={1997},
}
Pavel Exner, and SA Vugalter. Bound states in a locally deformed waveguide: the critical case. 1997. Vol. 39. In Letters in Mathematical Physics. pp.59-68. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020122733744528569.
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