GROWTH AND DIFFERENCE PROPERTIES OF MEROMORPHIC SOLUTIONS ON DIFFERENCE EQUATIONS

Abstract

Consider the difference Riccati equation $f(z+1)=\frac{a(z)f(z)+b(z)}{c(z)f(z)+d(z)}$, where $a,~b,~c,~d$ are polynomials, we precisely estimate growth of meromorphic solutions. To the difference Riccati equation $f(z+1)=\frac{A(z)+f(z)}{1-f(z)}$, where $A(z)=\frac{m(z)}{n(z)},$ $m(z),~n(z)$ are irreducible nonconstant polynomials, we precisely estimate exponents of convergence of zeros and poles of meromorphic solutions $f(z)$, their differences $\Delta f(z)=f(z+1)-f(z)$ and divided differences $\frac{\Delta f(z)}{f(z)}$.