On nonlinear elliptic equations with Hardy potential and L^{1}-data

We consider a class of nonlinear elliptic equations involving the Hardy potential and lower order terms whose simplest model is $$\begin{aligned} -\Delta u +b(|u|)|\nabla u|^{2}+\nu |u|^{s-1}u=\lambda \frac{u}{|x|^{2}}+f \end{aligned}$$ in a bounded open $\varOmega $ of $\mathbf{R }^{N}, N\ge 3,$ containing the origin, $s>\frac{N}{N-2}, \nu $ and $\lambda $ are positive real numbers. We prove that the presence of the term $\nu |u|^{s-1}u$ has an effect on the existence of solutions when $f\in L^{1}(\varOmega )$ assuming only that $b\in L^{1}(\mathbf{R })$ without any sign condition (i.e. $b(s)s\ge 0$ ).