On Growth of Meromorphic Solutions for Linear Difference Equations

Abstract

We mainly study growth of linear difference equations $P_n(z)f(z+n)+\cdots +P_{\mathrm{1}}(z)f(z+\mathrm{1})+P_{\mathrm{0}}(z)f(z)=\mathrm{0}$ and $P_n(z)f(z+n)+\cdots +P_{\mathrm{1}}(z)f(z+\mathrm{1})+P_{\mathrm{0}}(z)f(z)=F(z),$ where $F(z),P_{\mathrm{0}}(z),\dots ,P_n(z)$ are polynomials such that $F(z)P_{\mathrm{0}}(z)P_n(z)\not\equiv \mathrm{0}$ and give the most weak condition to guarantee that orders of all transcendental meromorphic solutions of the above equations are greater than or equal to 1.