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

Ignat, Radu, Nguyen, Luc, Slastikov, Valeriy and Zarnescu, Arghir (2014) Uniqueness results for an ODE related to a generalized Ginzburg-Landau model for liquid crystals. SIAM Journal on Mathematical Analysis, 46 (5). pp. 3390-3425. ISSN 0036-1410

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Abstract

We study a singular nonlinear ordinary differential equation on intervals {[}0, R) with R <= +infinity, 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.

Item Type: Article
Keywords: singular differential equations; nodal solutions; uniqueness; maximum principle; Ginzburg-Landau; liquid crystals
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Subjects: Q Science > QA Mathematics > QA0299 Analysis. Including analytical methods connected with physical problems
Depositing User: Arghir Zarnescu
Date Deposited: 13 Mar 2015 10:35
Last Modified: 07 Mar 2017 06:25
URI: http://sro.sussex.ac.uk/id/eprint/53358

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