The paper discusses the existence of positive solutions, dead core solutions and pseudodead core solutions of the singular Dirichlet problem ${\left(\phi \left(u^{\text{'}}\right)\right)}^{\text{'}}=\lambda f(t,u,u^{\text{'}})$, $u\left(0\right)=u\left(T\right)=A$. Here $\lambda$ is the positive parameter, $A>0$, $f$ is singular at the value $0$ of its first phase variable and may be singular at the value $A$ of its first and at the value $0$ of its second phase variable.