Degenerate nonlinear elliptic equations with Hardy potential and nonlinear convection term

We study degenerate nonlinear elliptic operators in the divergence form, taking into account the presence of a nonlinear convection term with growth properties and the Hardy potential. We investigate the interaction of these two terms on the existence and regularity of distributional solutions. More specifically, we establish two separate theorems about the existence of distributional solutions. The first result accounts for the convection term’s effect, while the second accounts for the term’s singularity at the origin. Furthermore, our second result expands and improves on some of the previous results in the literature by using a slightly modified proof.