On the structure of radial solutions for some quasilinear elliptic equations

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).