Relations between Solutions of Differential Equations and Small Functions. (25th March 2012) - Liu, Wei; Chen, Zong-Xuan
Abstract : We investigate relations between solutions, their derivatives of differential equation f ( k ) + A k − 1 f ( k − 1 ) + ⋯ + A 1 f ' + A 0 f = 0, and functions of small growth, where A j ( j = 0, 1, …, k − 1 ) are entire functions of finite order. By these relations, we see that every transcendental solution and its derivative of above equation have infinitely many fixed points.