Selfsimilar shrinking curves for anisotropic curvature flow equations (Q1344806)

The authors consider the second order differential equation (1) \(u'' + u - a (\theta)/u = 0\) in \(\mathbb{R}^ 1\), with a given positive function. This equation arises in describing selfsimilar solutions of anisotropic curvature flow equations. The main purpose of this article is to prove the existence of a \(T\)-periodic solution of (1) when \(a(\theta)\) is continuous and \(T\)-periodic, and the uniqueness of the periodic solution when \(T = \pi\).