What are the existing results on the $C^{0}$ estimate of the solution of the semi-linear pde $\Delta u = f(x,u,\nabla u)$.

Question

I have read several papers but their conditions are so strong which always assume that $f(x,z,\eta)$ is controlled by $\left| \eta \right|$, for example: $\left| f\right| \leq C(\left| \eta \right|^{2}+g(x))$

What I want to ask is that if there are any better results about the $C^{0}$ estimate I still don't know.