On global existence of an implicit function

The problem of global existence of an implicit function is studied, i.e., the properties of Banach spaces $X$, $Y$, $Z$ and functions
$$ F\colon X\times Y\to Z, $$
for which a smooth solution $y=\varphi(x)$ of the equation $F(x,y) = 0$ is possible with given initial condition $y_0=\varphi(x_0)$, where $ F(x_0,y_0)=0$. It is shown that excessive smoothness of $F$ with respect to $y$ is necessary for the existence of a smooth global solution (in comparison with a local solution).