How does the nonlinearity growth affect the regularity of solutions?

Question

Consider equation \begin{equation*} \begin{cases} -\Delta u=f(u)&\text{ in }\Omega,\\ u=0 &\text{ on }\partial\Omega, \end{cases} \end{equation*} where $|f(u)|\leqslant C_1+C_2|u|^{p-1}, p<{2N\over N-2}$, $\Omega\subset \mathbb{R}^N$ is a bounded domain. How does growth condition use in the argument of regularity of solutions? For example, how to use this growth condition to prove solution $u\in L^{\infty}_{loc}$? What role does the growth condition play?