Existence of sign-changing solutions for radially symmetric p-Laplacian equations with various potentials

Abstract

In this article, we study the nonlinear equation (rn-1|u′(r)|p-2u′(r))′ + rn-1w(r)|u(r)|q-2 u(r) = 0, where q > p > 1. For positive potentials (w > 0), we investigate the existence of sign-changing solutions with prescribed number of zeros depending on the increasing initial parameters. For negative potentials, we deduce a finite interval in which the positive solution will tend to infinity. The main methods using in this work are the scaling argument, Prüfer-type substitutions, and some integrals involving the p-Laplacian.