Uniqueness results for an ODE related to a generalized Ginzburg-Landau   model for liquid crystals
  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. 
Radu Ignat, Luc Nguyen, Valeriy Slastikov and Arghir Zarnescu
math.AP math.CA