Semi-classical states for logarithmic Schrödinger equations

Norihisa Ikoma, Kazunaga Tanaka, Zhi Qiang Wang, Chengxiang Zhang

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we investigate semi-classical bound states for logarithmic Schrödinger type equations with a potential function which has a finite number of singularities of at most logarithmic strength. We construct localized solutions concentrating at a logarithmic type singular point of the potential, and we also characterize the asymptotic limiting profile of the localized solutions. To accomplish these, we develop new penalization techniques for treating the difficulties associated with the non-smoothness of the variational formulation and the singularity of the potentials.

Original languageEnglish
Pages (from-to)1900-1942
Number of pages43
JournalNonlinearity
Volume34
Issue number4
DOIs
Publication statusPublished - 2021 Apr

Keywords

  • Logarithmic nonlinearity
  • Logarithmic singular potential
  • Semi-classical states of Schrödinger equations

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Applied Mathematics

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