A dynamical approach to the study of radial solutions for $p$-Laplace equation

In this paper we give a survey of the results concerning the existence of ground states and singular ground states for equations of the following form: $$Delta_{p}u+ f(u,| extbf{x}|)=0$$ where $Delta_{p}u=div(|Du|^{p-2}Du)$, $p>1$ is the $p$-Laplace operator, $ extbf{x} in RR^n$ and $f$ is continuous, and locally Lipschitz in the $u$ variable. We focus our attention mainly on radial solutions. The main purpose is to illustrate a dynamical approach, which involves the introduction of the so called Fowler transformation. This technique turns to be particularly useful to analyze the problem, when $f$ is spatial dependent, critical or supercritical and to detect singular ground states.