Crossed differential systems of equations and Clunie lemma

Abstract

We study properties of transcendental meromorphic solutions of crossed complex differential systems of equations. For instance, we study the crossed Riccati differential system $$\displaylines{ f(z)^2=1-g'(z), \cr g(z)^2=1-f'(z), }$$ and the crossed Weierstrass differential system $$\displaylines{ f(z)^3=1-g'(z)^2, \cr g(z)^3=1-f'(z)^2. }$$ In addition, we establish a crossed version of Clunie lemma. For more information see https://ejde.math.txstate.edu/Volumes/2024/52/abstr.html