Abstract
In this paper, we investigate the growth of transcendental meromorphic solutions of some types of systems of complex functional equations and obtain the lower bounds for Nevanlinna lower order for meromorphic solutions of such equations. Our results are improvement of the previous theorems given by Gao, Zheng and Chen. Some examples are also given to illustrate our results.MSC:39A50, 30D35.
Highlights
Introduction and main resultsThroughout this paper, the term ‘meromorphic’ will always mean meromorphic in the complex plane C
Considering a meromorphic function f, we shall assume that readers are familiar with the fundamental results and the standard notations of the Nevanlinna value distribution theory of meromorphic functions such as m(r, f ), N(r, f ), T(r, f ), the first and second main theorems, lemma on the logarithmic derivatives etc. of Nevanlinna theory
There have been a number of papers focusing on the growth of solutions of difference equations, value distribution and uniqueness of differences analogues of Nevanlinna’s theory
Summary
Introduction and main resultsThroughout this paper, the term ‘meromorphic’ will always mean meromorphic in the complex plane C. In , Silvennoinen [ ] studied the growth and existence of meromorphic solutions of functional equations of the form f (p(z)) = R(z, f (z)) and obtained the following result. [ , Theorem ] Let (f , f ) be a non-constant meromorphic solution of system ( ).
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