Growth of solutions of non-homogeneous linear differential equations and its applications
Main Article Content
Abstract
In this paper, we investigate the growth properties of solutions of the non-homogeneous linear complex differential equation $L\left(f\right)=b\left(z\right)f+c\left(z\right)$, where $L\left(f\right)$ is a linear differential polynomial and $b\left( z\right) $, $c\left( z\right) $ are entire functions and give some of its applications on sharing value problems.
Article Details
References
[1] B. Bela ̈ıdi, Estimation of the hyper-order of entire solutions of complex linear ordinary differential equations whose coefficients are entire functions, Electronic journal of qualitative theory of differential equations (EJQTDE) 5 (2002) , 1–8. Google Scholar
[2] W. Cherry, Z. Ye, Nevanlinna’s Theory of Value Distribution, Springer Verlag, 2001. Google Scholar
[3] X. Chen, H. G. Tian, W. J. Yuan, W. Chen, Normality criteria of Lahiris type concerning shared values. J Jiangxi Norm Univ Nat Sci 38 (2014), 37–41. Google Scholar
[4] G. Gundersen, Estimates for the logarithmic derivative of a meromorphic function, plus similar estimates, Journal of the London Mathematical Society 37 (2) (1998) , 88–104. Google Scholar
[5] W. K. Hayman, Meromorphic Functions, The Clarendon Press, Oxford, 1964. Google Scholar
[6] W. K. Hayman, The local growth of power series: a survey of the Wiman-Valiron method, Canadian Mathematical Bulletin 17 (1974) , 317–358. Google Scholar
[7] Y. Z. He and X. Z. Xiao, Algebroid functions and ordinary differential equations, Science Press, Beijing, 1988. Google Scholar
[8] I. Laine, Nevanlinna Theory and Complex Differential Equations, Walter de Gruyter, Berlin New York, 1993. Google Scholar
[9] X. M. Li, H. X. Yi, An entire function and its derivatives sharing a polynomial. J Math Anal Appl 330 (2007), 66–79. Google Scholar
[10] L. W. Liao, The new developments in the research of nonlinear complex differential equations. J Jiangxi Norm Univ Nat Sci 39 (2015), 331–339. Google Scholar
[11] Mues E. Mues , N. Steinmetz, Meromorphe funktionen, die mit ihrer ersten und zweiten Ableitung einen endlichen Wertteilen, Complex Var Theory Appl 6 (1986), 51–71. Google Scholar
[12] G. Valiron, Lectures on the General Theory of Integral Functions, Chelsea, New York, 1949. Google Scholar
[13] L. Yang, Value distribution Theory, Springer-Verlag, Berlin, 1993. Google Scholar
[14] Q. C. Zhang, Meromorphic function that shares one small function with its derivative, J Inequal Pure Appl Math 6 (Art.116)(2005), 1–13. Google Scholar
[15] J. L. Zhang, L. Z. Yang, A power of a meromorphic function sharing a small function with its derivative, Ann Acad Sci Fenn Math 34 (2009), 249–260. Google Scholar
[16] X. Z. Zhao, The uniqueness of meromorphic functions and their derivatives weighted-sharing the sets of small functions, J Jiangxi Norm Univ Nat Sci. 36 (2012), 141–146. Google Scholar