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Zeros, poles, and fixed points of solution and its difference for some types of difference equations. (English) Zbl 1464.39016

Summary: The main purpose of this paper is studying some properties on the growth and value distribution of solutions of some difference equations. We obtain some results on the existence and estimates of growth of solutions \(f\) for some difference equations and some estimates of the exponent of convergence of poles of \(\varDelta f,\varDelta^2f,\varDelta f/f\), and \(\varDelta^2 f/f\), which improve and extend the previous results given by Z.-X. Chen [Kodai Math. J. 34, No. 2, 244–256 (2011; Zbl 1246.30058)], Q. Li and Z.-B. Huang [Adv. Difference Equ. 2015, Paper No. 276, 11 p. (2015; Zbl 1345.30033)]. Moreover, we also give some examples to show the extension of solutions of some equations.

MSC:

39A45 Difference equations in the complex domain
30D35 Value distribution of meromorphic functions of one complex variable, Nevanlinna theory
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