Singular boundary value problems of a porous media logistic equation (Q1885292)

In the present study the authors deal with the existence, the blow up rate and the uniqueness of the classical positive solutions to the singular boundary value problem \[ -\Delta u=W(x)u^q-a(x)f(u)\text{ in }\Omega\quad u=\infty\text{ on }\partial\Omega,\tag{1} \] where \(\Omega\) is a bounded domain of \(\mathbb R^N\), \(N\geq 1\), \(W\in L^\infty (\Omega)\), \(0<q<1\), and \(a(x)\) satisfies some structural assumption. Under some natural assumption on \(f\), the authors achieve their goals.