Asymptotic behaviors of Green-Sch potentials at infinity and its applications

Lei Qiao, Lee Deville

Research output: Contribution to journalArticlepeer-review


The first aim in this paper is to deal with asymptotic behaviors of Green-Sch potentials in a cylinder. As an application we prove the integral representation of nonnegative weak solutions of the stationary Schrödinger equation in a cylinder. Next we give asymptotic behaviors of them outside an exceptional set. Finally we obtain a quantitative property of rarefied sets with respect to the stationary Schrödinger operator at +∞ in a cylinder. Meanwhile we show that the reverse of this property is not true.

Original languageEnglish (US)
Pages (from-to)2321-2338
Number of pages18
JournalDiscrete and Continuous Dynamical Systems - Series B
Issue number6
StatePublished - Aug 2017


  • Asymptotic behavior
  • Green-Sch potential
  • Stationary Schrödinger operator

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


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