What is the class of solutions for the differential equation (with $t \in \mathbb{R}$):
$$y'(t) = \frac{1}{2}y''(2y(t))?$$
In the previous equation, the second derivative of $y$ is evaluated in $2y(t)$ (it is not the multiplication of $y''(t)$ with $y(t)$).
Generally, I would be interested in references about this kind of differential equations involving recurrence.