Electronic Journal of Differential Equations, Vol. 2021 (2021), No. 40, pp. 1-13.

Title: Existence of sign-changing solutions for radially symmetric p-Laplacian equations
       with various potentials
       
Author: Wei-Chuan Wang (National Quemoy Univ., Kinmen, Taiwan)

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.

Submitted September 8, 2020. Published May 07, 2021.
Math Subject Classifications: 34A12, 34B15, 34A55.
Key Words: Nonlinear p-Laplacian equation; sign-changing solution; blow-up solution.