On a singular nonlinear Dirichlet problem with a convection term (Q2706218)

The authors establish some results on existence, nonxistence, and regularity of a positive solution to the following Dirichlet problem NEWLINE\[NEWLINE -\Delta u=\frac{1}{u^{\alpha}+ \lambda |\nabla u|^p+\sigma}, \quad x \in \Omega \subset \mathbb{R}^n,NEWLINE\]NEWLINE \(u|_{\partial \Omega}=0. \) Under some conditions on parameters, uniqueness of a classical solution is shown. Additionally, some open problems of the theory of this boundary value problem are solved. The approach is based on existence regularity theory and a subsolution-supersolution method.