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 <= +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.