On the growth of solutions of a class of higher order linear differential equations with coefficients having the same order

• Published in: Journal of mathematical analysis and applications Vol. 340; no. 1; pp. 487 - 497
• Main Authors: Tu, Jin, Yi, Cai-Feng
• Format: Journal Article
• Language: English
• Published: San Diego, CA Elsevier Inc 01.04.2008; Elsevier
• Subjects: Entire function; Exact sciences and technology; Functions of a complex variable; Hyper order; Linear differential equations; Mathematical analysis; Mathematics; Ordinary differential equations; Sciences and techniques of general use; Type; Hyper order; Type; Linear differential equations; Entire function; Second order; Linear equation; Mathematical analysis; Differential equation; Application; Non existence
• ISSN: 0022-247X; 1096-0813
• DOI: 10.1016/j.jmaa.2007.08.041

In this paper, the authors investigate the growth of solutions of a class of higher order linear differential equations f ( k ) + A k − 1 f ( k − 1 ) + ⋯ + A 0 f = 0 when most coefficients in the above equations have the same order with each other, and obtain some results which improve previous results due to K.H. Kwon [K.H. Kwon, Nonexistence of finite order solutions of certain second order linear differential equations, Kodai Math. J. 19 (1996) 378–387] and Z.-X. Chen [Z.-X. Chen, The growth of solutions of the differential equation f ″ + e − z f ′ + Q ( z ) f = 0 , Sci. China Ser. A 31 (2001) 775–784 (in Chinese); Z.-X. Chen, On the hyper order of solutions of higher order differential equations, Chinese Ann. Math. Ser. B 24 (2003) 501–508 (in Chinese); Z.-X. Chen, On the growth of solutions of a class of higher order differential equations, Acta Math. Sci. Ser. B 24 (2004) 52–60 (in Chinese); Z.-X. Chen, C.-C. Yang, Quantitative estimations on the zeros and growth of entire solutions of linear differential equations, Complex Var. 42 (2000) 119–133].