Existence and optimal estimates of solutions for singular nonlinear Dirichlet problems (Q1879685)

The goal of this paper is to study the existence and asymptotic estimates of classical solutions to the model problems \[ -\Delta_xu= \kappa(x)g(u), \quad x\in\Omega, \qquad u>0, \quad\text{in }\Omega, \qquad u=0, \quad\text{on }\partial\Omega, \tag{1} \] where \(\Omega\) is a bounded domain with \(C^2\)-boundary in \(\mathbb R^N\) \((N\geq 1)\), and \(\kappa(x)\), \(g(\cdot)\) satisfies some natural assumptions, including in particular, that (2) \(\lim_{s\to+0} g(s)= +\infty\).