A further study on Markus's conjecture

Abstract The paper concerns the algebraic differential independence of meromorphic solutions of difference equation , where is a rational function with a certain condition. Based on ideas by Bank and Kaufman [Funkcial. Ekvac. 19 (1976), 53–63; Math Ann. 232 (1978), 115–120] and Wang and Yao [J. Differ. Equations. 412 (2024), 797–807], we confirm that Markus's conjecture holds in a more general form. Meanwhile, an example is given to show that the condition on is necessary.