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Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article On the Growth of Solutions of Some Second-Order Linear Differential Equations | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2011 Article ID 635604 9 pages doi 10.1155 2011 635604 Research Article On the Growth of Solutions of Some Second-Order Linear Differential Equations Feng Peng and Zong-Xuan Chen School of Mathematical Sciences South China Normal University Guangzhou 510631 China Correspondence should be addressed to Zong-Xuan Chen chzx@vip.sina.com Received 10 December 2010 Accepted 9 February 2011 Academic Editor Alberto Cabada Copyright 2011 F. Peng and Z.-X. Chen. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. We investigate the growth of solutions of f P z f Q z f 0 where P z and Q z are entire functions. When P z e z and Q z A1 z ea1 z A2 z ea2z satisfy some conditions we prove that every nonzero solution of the above equation has infinite order and hyper-order 1 which improve the previous results. 1. Introduction and Results In this paper we will assume that the reader is familiar with the fundamental results and the standard notations of the Nevanlinna s value distribution theory of meromorphic functions e.g. see 1-3 . In addition we will use the notation Ơ f to denote the order of growth of meromorphic function f z ơ2 f to denote the hyper-order of f z see 3 . Ơ2 f is defined to be Ulf Slogl gT M. 1.1 7 r X log r We consider the second-order linear differential equation f P z f Q z f 0 1.2 where P z and Q z are entire functions of finite order. It is well known that each solution of 1.2 is an entire function and most solutions of 1.2 have infinite order. 2 Journal of Inequalities and Applications Thus a natural question is what conditions on P z and Q z will guarantee that every solution f 0 of 1.2 has infinite order Ozawa 4 Gundersen 5 Amemiya and Ozawa 6 and Langley 7 have studied the problem with P z e z and Qfz is complex number .
