We prove the $$C^{1,\beta }$$ C1,β -boundary regularity and a comparison principle for weak solutions of the problem $$\begin{aligned} \left\{ \begin{array}{ll} -\Delta _{p}u-\lambda \psi _{p}(u)=f(x)&{}\quad \text {in }\Omega , \\ u=0&{}\quad \text {on }\partial \Omega , \end{array} \right. \end{aligned}$$ -Δpu-λψp(u)=f(x)inΩ,u=0on∂Ω, where $$\Omega $$ Ω is a bounded domain in $$\mathbb {R}^{N},N>1\ $$ RN,N>1 with smooth boundary $$\partial \Omega ,\ \ \Delta _{p}u=\mathrm{div}(|\nabla u|^{p-2}\nabla u),\psi _{p}(u)=|u|^{p-2}u,p>1,\ $$ ∂Ω,Δpu=div(|∇u|p-2∇u),ψp(u)=|u|p-2u,p>1, and f is allowed to be unbounded.