Positive solutions of nonlinear elliptic singular boundary value problems in a ball.
The authors deal with the existence of positive solutions of the following singular nonlinear elliptic boundary value problem \[ \begin{cases} \Delta u+f(x,\nabla u)u^{-\lambda}=0,\quad & x\in B\subset\mathbb{R}^N\\ u=0,\quad & x\in\partial B,\end{cases}\tag{1} \] where \(B=\{x\in\mathbb{R}^N \mid|x|<1\}\) and \(\nabla\) denote the \(N\)-dimensional gradient operator. The main goal of the authors is to prove existence of positive solutions of (1) belonging to \(C^2(B)\cap C(\overline B)\).
scientific article; zbMATH DE number 2103983