## Problems for elliptic singular equations with a gradient term.(English)Zbl 1103.35031

The author studies the Dirichlet problem $$\Delta u+g(u)| \nabla u| ^q +f(u)=0$$ in $$D$$, $$u=0$$ on $$\partial D$$, where $$D$$ is a bounded smooth domain in $$\mathbb R^n$$, $$0<q<2$$, $$g(t)$$ is a decreasing smooth function in $$(0,\infty )$$ and $$f(t)$$ is a decreasing and positive smooth function in $$(0,\infty )$$, which approaches infinity as $$t\to \infty$$. The existence and uniqueness of a positive classical solution of the problem is proved. The asymptotic behaviour of a solution near the boundary is studied.

### MSC:

 35J60 Nonlinear elliptic equations 35B40 Asymptotic behavior of solutions to PDEs 35J25 Boundary value problems for second-order elliptic equations
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### References:

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