Existence of radial solutions for the $p$-Laplacian elliptic equations with weights

Abstract

Using the definition of solution and the qualitative properties established in the recent paper [17], some existence results are obtained both for crossing radial solutions and for positive or compactly supported radial ground states in $\mathbb R^n$ of quasilinear singular or degenerate elliptic equations with weights and with non--linearities which can be possibly singular at $x=0$ and $u=0$, respectively. The technique used is based on the papers [1] and [12]. Furthermore we obtain a non--existence theorem for radial ground states using a technique of Ni and Serrin [13].