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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 \(\Omega\).

MSC:

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