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

2014/04/07 by Radu Ignat, Luc Nguyen, Ignat, Radu +5 · 1 citation
Mathematics · #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #math.AP #math.CA

paper · pdf · doi:10.48550/arxiv.1404.1724

arxiv created 2014/04/07 · arxiv updated 2014/04/08

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.

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