Entire solutions of $q$-difference equations and value distribution of $q$-difference polynomials
Volume 109 / 2013
Annales Polonici Mathematici 109 (2013), 39-46
MSC: Primary 39A05; Secondary 30D35.
DOI: 10.4064/ap109-1-3
Abstract
We investigate the existence and uniqueness of entire solutions of order zero of the nonlinear $q$-difference equation of the form $f^n(z) + L(z) = p(z)$, where $p(z)$ is a polynomial and $L(z)$ is a linear differential-$q$-difference polynomial of $f$ with small growth coefficients. We also study the zeros distribution of some special type of $q$-difference polynomials.
