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