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

Abstract

In this article, we study the nonlinear equation $$ \big(r^{n-1}|u'(r)|^{p-2}u'(r)\big)'+r^{n-1}w(r)|u(r)|^{q-2}u(r)=0, $$ 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, Prufer-type substitutions, and some integrals involving the p-Laplacian. For more information see https://ejde.math.txstate.edu/Volumes/2021/40/abstr.html