Meromorphic solutions of some complex non-linear difference equations
This nice paper studies the growth and the zeros of meromorphic solutions of the functional equation \[f^2(z + 1) + A_1(z)f(z + 1)f(z) + A_2(z)f^2(z) = A_3(z),\] where \(A_1(z), A_2(z), A_3(z)\) are polynomials and \(A_3(z)\neq 0\). To do this, the authors use Nevalinna theory. The results are quite technical and the same holds with the proofs. The paper is direct continuation of the research of \textit{Y. Liu} [J. Appl. Math. Comput. 61, No. 1--2, 337--348 (2019; Zbl 1427.30060)] and \textit{Z. Chen} [Sci. China, Math. 54, No. 10, 2123--2133 (2011; Zbl 1238.30019)].
scientific article; zbMATH DE number 7377552
scientific article