Existence and optimal estimates of solutions for singular nonlinear Dirichlet problems
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) \(\lim_{s\to+0} g(s)= +\infty\).
scientific article; zbMATH DE number 2102517
scientific article