Growth of solutions of a class of complex differential equations
Volume 95 / 2009
Annales Polonici Mathematici 95 (2009), 141-152
MSC: Primary 34M10; Secondary 30D35.
DOI: 10.4064/ap95-2-5
Abstract
The main purpose of this paper is to partly answer a question of L. Z. Yang [Israel J. Math. 147 (2005), 359–370] by proving that every entire solution $f$ of the differential equation $f^{\prime }-e^{P(z)}f=1$ has infinite order and its hyperorder is a positive integer or infinity, where $P$ is a nonconstant entire function of order less than ${1/2}.$ As an application, we obtain a uniqueness theorem for entire functions related to a conjecture of Brück [Results Math. 30 (1996), 21–24].
