Uniqueness results for an ODE related to a generalized Ginzburg-Landau model for liquid crystals
Analysis of PDEs
2014-04-08 v1 Classical Analysis and ODEs
Abstract
We study a singular nonlinear ordinary differential equation on intervals with , 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.
Keywords
Cite
@article{arxiv.1404.1724,
title = {Uniqueness results for an ODE related to a generalized Ginzburg-Landau model for liquid crystals},
author = {Radu Ignat and Luc Nguyen and Valeriy Slastikov and Arghir Zarnescu},
journal= {arXiv preprint arXiv:1404.1724},
year = {2014}
}