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: Δpu + f (u, |x|) = 0 where Δpu = div(|Du| p-2 Du), p > 1 is the p-Laplace operator, x ∈ ℝn 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.