Growth and value distribution of linear difference polynomials generated by meromorphic solutions of higher-order linear difference equations

Abstract

In this article, we investigate the relationship between growth and value distribution of meromorphic solutions for the higher-order complex linear difference equations $$ A_n(z)f(z+n)+\dots+A_1(z)f(z+1)+A_0(z)f(z)=0 \quad \text{and } =F(z), $$ and for the linear difference polynomial $$ g(z)=\alpha_n(z)f(z+n)+\dots+\alpha_1(z)f(z+1)+\alpha_0(z)f(z) $$ generated by \(f(z)\) where \(A_j(z)\), \(\alpha_j(z)\) (\(j=0,1,\ldots,n\)), \(F(z)\) \((\not\equiv0)\) are meromorphic functions. We improve some previous results due to Belaidi, Chen and Zheng and others. For more information see https://ejde.math.txstate.edu/Volumes/2023/84/abstr.html