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Journal Articles SIAM Journal on Mathematical Analysis Year : 2014

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

Radu Ignat
Valeriy Slastikov
  • Function : Author
Arghir Zarnescu
  • Function : Author

Abstract

We study a singular nonlinear ordinary differential equation on intervals $[0,R)$ with $R\le +\infty$, 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.

Dates and versions

hal-01673414 , version 1 (29-12-2017)

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Radu Ignat, Luc Nguyen, Valeriy Slastikov, Arghir Zarnescu. Uniqueness results for an ODE related to a generalized Ginzburg-Landau model for liquid crystals. SIAM Journal on Mathematical Analysis, 2014, ⟨10.1137/130948598⟩. ⟨hal-01673414⟩
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