Uniqueness results for an ODE related to a generalized Ginzburg-Landau model for liquid crystals

Radu Ignat*, Luc Nguyen, Valeriy Slastikov, Arghir Zarnescu

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

16 Citations (Scopus)

Abstract

We study a singular nonlinear ordinary differential equation on intervals [0,R) with R ≤ +∞, motivated by the Ginzburg-Landau models in superconductivity and Landau-de Gennes models in liquid crystals. We prove existence and uniqueness of positive solutions under general assumptions on the nonlinearity. Further uniqueness results for sign-changing solutions are obtained for a physically relevant class of nonlinearities. Moreover, we prove a number of fine qualitative properties of the solution that are important for the study of energetic stability.

Original languageEnglish
Pages (from-to)3390-3423
Number of pages34
JournalSIAM Journal on Mathematical Analysis
Volume46
Issue number5
DOIs
Publication statusPublished - 2014

Keywords

  • Ginzburg-Landau
  • Liquid crystals
  • Maximum principle
  • Nodal solutions
  • Singular differential equations
  • Uniqueness

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