The authors investigate necessary and sufficient conditions for the existence of nonnegative solutions of the \(p\)-Laplacian boundary blow-up problem \[ (\varphi_p(u'))'=\lambda f(u),\quad 0<x<1,\quad \lim_{x\to^0+}u(x)=\infty=\lim_{x\to 1^-}u(x), \] where \(p>1\), \(\varphi_p(u)=|u|^{p-2}u\), \(\lambda\) is a positive bifurcation parameter. The explicit necessary and sufficient conditions for the existence of nonnegative solutions of boundary blow-up problem are given. The gap is extremely small between the explicit necessary condition and the explicit sufficient for the existence of nonnegative solutions.