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arXiv · 1404.1724

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

Radu Ignat·Luc Nguyen·Valeriy Slastikov·Arghir Zarnescu
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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.

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Radu Ignat, Luc Nguyen, Valeriy Slastikov, Arghir Zarnescu. 2014-04-07. Uniqueness results for an ODE related to a generalized Ginzburg-Landau model for liquid crystals. https://arxiv.org/abs/1404.1724

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