GROWTH OF MEROMORPHIC SOLUTIONS TO HOMOGENEOUS AND NON-HOMOGENEOUS LINEAR (DIFFERENTIAL-)DIFFERENCE EQUATIONS WITH MEROMORPHIC COEFFICIENTS

In this article, we study the growth of meromorphic solutions of homogeneous and non-homogeneous linear difference equations and linear differential-difference equations. When there exists only one coefficient having the maximal iterated order or having the maximal iterated type among those having the maximal iterated order, and the above coefficient satisfies certain conditions on its poles, we obtain estimates on the lower bound of the iterated order of the meromorphic solutions. The case p = 1 is also discussed and corresponding results are obtained by strengthening some conditions.

[1]  Z. Latreuch.  GROWTH AND OSCILLATION OF MEROMORPHIC SOLUTIONS OF LINEAR DIFFERENCE EQUATIONS , 2014 .

[2]  X. Zheng,et al.  Growth of Meromorphic Solutions of Complex Linear Differential-Difference Equations with Coefficients Having the Same Order , 2014 .

[3]  K. Shon,et al.  On Growth of Meromorphic Solutions for Linear Difference Equations , 2013 .

[4]  Zhiqiang Mao,et al.  On the meromorphic solutions of some linear difference equations , 2013, Advances in Differential Equations.

[5]  X. Zheng,et al.  Growth of meromorphic solutions of linear difference equations , 2011 .

[6]  Zongsheng Gao,et al.  Finite order meromorphic solutions of linear difference equations , 2011 .

[7]  Zong-Xuan Chen.  Growth and zeros of meromorphic solution of some linear difference equations , 2011 .

[8]  Ting-Bin Cao,et al.  On the meromorphic solutions of linear differential equations on the complex plane , 2010 .

[9]  Chung-Chun Yang,et al.  Clunie theorems for difference and q‐difference polynomials , 2007 .

[10]  Y. Chiang,et al.  On the Nevanlinna characteristic of f(z+η) and difference equations in the complex plane , 2006, math/0609324.

[11]  R. Korhonen,et al.  Nevanlinna theory for the difference operator , 2005, math/0506011.

[12]  Lo Yang,et al.  Value Distribution Theory , 1993 .

[13]  Ilpo Laine,et al.  Nevanlinna Theory and Complex Differential Equations , 1992 .

[14]  F. Gross.  On the distribution of values of meromorphic functions , 1968 .

[15]  W. K. Hayman,et al.  On the characteristic of functions meromorphic in the unit disk and of their integrals , 1964 .

[16]  D. Sato.  On the rate of growth of entire functions of fast growth , 1963 .