On the structure of radial solutions for some quasilinear elliptic equations

TL;DR

This paper investigates the structure of entire radial solutions to certain quasilinear p-Laplace equations with radial weights, focusing on solutions that vanish at infinity, extending previous results in the field.

Contribution

It extends previous work by analyzing the structure of solutions that tend to zero at infinity for a class of quasilinear elliptic equations with radial weights.

Findings

Characterization of solutions that vanish at infinity.

Extension of Tang's (2001) results to broader classes of solutions.

Insights into the behavior of positive and sign-changing solutions at infinity.

Abstract

In this paper we study entire radial solutions for the quasilinear $p$-Laplace equation $\Delta_p u + k(x) f(u) = 0$ where $k$ is a radial positive weight and the nonlinearity behaves e.g. as $f(u)=u|u|^{q-2}-u|u|^{Q-2}$ with $q<Q$. In particular we focus our attention on solutions (positive and sign changing) which are infinitesimal at infinity, thus providing an extension of a previous result by Tang (2001).