Qualitative Properties of Solutions to a PDE Problem Involving a Singular Potential Term

Abstract

This paper addresses some properties of solutions to a PDE problem characterized by a singular coefficient
$$
\Delta_p U-\alpha x.\nabla U+ \frac{|U|^{q-1}U}{|x|^{2} }=0\quad \text{in} \quad \mathbb{R}^N,
$$ where $p>2$, $q\geq 1$, $N>2$, and $\alpha >0$.\\
The analysis deals with proving the existence of global solutions and characterizing the asymptotic properties of some solutions.