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Subnormal transcendental meromorphic solutions of difference equations with Schwarzian derivative
M. T. Xia, J. R. Long, X. X. Xiang
https://arxiv.org/abs/2510.10626 https://

Subnormal transcendental meromorphic solutions of difference equations with Schwarzian derivative
The existence of subnormal solutions of following three difference equations with Schwarzian derivative $$ω(z+1)-ω(z-1)+a(z)(S(ω,z))^n=R(z,ω(z)),$$ $$ω(z+1)ω(z-1)+a(z)S(ω,z)=R(z,ω(z)),$$ and $$(ω(z)ω(z+1)-1)(ω(z)ω(z-1)-1)+a(z)S(ω,z)=R(z,ω(z))$$ are studied by using Nevanlinna theory, where $n\ge 1$ is an integer, $a(z)$ is small with respect to $ω$, $S(ω,z)$ is Schwarzian derivative, $R(z,ω)$ is rational in $ω$ with small meromorphic coefficients with respect to $ω$. The nece…