Hi everyone, could someone help me give a characterization of $\Psi(z)$ such that

$$8\Psi''-4\frac{(\Psi')^2}{\Psi}-\theta(\Psi')^2\geq 0,\ \ \forall z\in\mathbb{R}$$

where

$$\Psi=\Psi(z),\ \ \Psi'=\Psi'(z),\ \ \Psi''=\Psi''(z)$$

and $\theta$ is some positive constant.

Many thanks!