In this paper, we are interested in the existence result of solutions for nonlinear and singular Dirichlet problem whose model is$$\begin{aligned} \left\{ \begin{aligned}&-\mathrm{div}\Big (b(u) \nabla u\Big )+\mu (x) \frac{|\nabla u|^2}{|u|^\theta } \mathrm{{sign}}(u)=f\ \ \mathrm{in}\ \Omega ,\\&u=0\ \ \mathrm{on}\ {\partial \Omega },\\ \end{aligned} \right. \end{aligned}$$where \(\Omega \) is a bounded open subset of \(\mathbb {R}^N (N\ge 2)\), b(s) is a positive continuous function which blows up for a finite value of the unknown, \(\mu (x)\) is positive, bounded and measurable, \(0<\theta < 1\), and the source f belongs to \(L^1(\Omega )\).

中文翻译：

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具有无界系数和奇异低阶项的非线性椭圆方程

在本文中，我们对模型为$$ \ begin {aligned} \ left \ {\ begin {aligned}＆-\ mathrm {div} \ Big（b（ u）\ nabla u \ Big）+ \ mu（x）\ frac {| \ nabla u | ^ 2} {| u | ^ \ theta} \ mathrm {{sign}}（u）= f \ \ \ mathrm { in} \ \ Omega，\\＆u = 0 \ \ \ mathrm {on} \ {\ partial \ Omega}，\\ \ end {aligned} \ right。\ end {aligned} $$其中\（\ Omega \）是\（\ mathbb {R} ^ N（N \ ge 2）\）的有界开放子集，b（s）是一个正连续函数，它会爆炸对于未知数的有限值，\（\ mu（x）\）是正的，有界且可测量的\（0 <\ theta <1 \），并且源f属于\（L ^ 1（\ Omega）\）。