Nonlinear elliptic equations with unbounded coefficient and singular lower order term

Abstract

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 $$L^1(\Omega )$$ .