Subnormal transcendental meromorphic solutions of difference equations with Schwarzian derivative

The existence of subnormal solutions of following three difference equations with Schwarzian derivative $$\omega (z+1)-\omega (z-1)+a(z)(S(\omega ,z){)}^n=R(z,\omega (z)),$$ $$\omega (z+1)\omega (z-1)+a(z)S(\omega ,z)=R(z,\omega (z)),$$ and $$(\omega (z)\omega (z+1)-1)(\omega (z)\omega (z-1)-1)+a(z)S(\omega ,z)=R(z,\omega (z))$$ are studied by using Nevanlinna theory, where $n\ge 1$ is an integer, $a(z)$ is small with respect to $\omega$, $S(\omega ,z)$ is Schwarzian derivative, $R(z,\omega )$ is rational in $\omega$ with small meromorphic coefficients with respect to $\omega$. The necessary conditions for the existence of subnormal transcendental meromorphic solutions of the above equations are obtained. Some examples are given to support these results.