Problems for elliptic singular equations with a quadratic gradient term. (English) Zbl 1156.35032

The authors study positive solutions of the following boundary value problem: \[ \begin{cases}\Delta u+ g(u)|\nabla u|^2+ f(u)= 0,\quad &\text{in }\Omega,\\ u= 0,\quad &\text{on }\partial\Omega,\end{cases} \] where \(\Omega\subset \mathbb{R}^d\), \(d\geq 2\); \(f(\cdot)\) and \(g(\cdot)\) are given functions. The goal of the authors is to get existence and uniqueness results and to describe the asymptotic near the boundary of \(\Omega\).


35J60 Nonlinear elliptic equations
35J25 Boundary value problems for second-order elliptic equations
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