Electron. J. Differential Equations, Vol. 2021 (2021), No. 40, pp. 1-13.

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

Wei-Chuan Wang

In this article, we study the nonlinear equation

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 7, 2021.
Math Subject Classifications: 34A12, 34B15, 34A55.
Key Words: Nonlinear p-Laplacian equation; sign-changing solution; blow-up solution.

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Wei-Chuan Wang Department of Civil Engineering and Engineering Management
Center for General Education
National Quemoy University
Kinmen, Taiwan 892, ROC
email: wangwc@nqu.edu.tw, wangwc72@gmail.com

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