On Stationary Solutions of the 2D Doi-Onsager Model

We study the 2D Doi–Onsager models with general potential kernel, with special emphasis on the classical Onsager kernel. Through application of topological methods from nonlinear functional analysis, in particular the Leray–Schauder degree theory, we obtain the uniqueness of the trivial solution for low temperatures as well as the local bifurcation structure of the solutions.