Existence of sign-changing solutions for radially symmetric p-Laplacian equations with various potentials
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Date
2021-05-07
Authors
Wang, Wei-Chuan
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
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.
Description
Keywords
Nonlinear p-Laplacian equation, Sign-changing solution, Blow-up solution
Citation
Wang, W. C. (2021). Existence of sign-changing solutions for radially symmetric p-Laplacian equations with various potentials. Electronic Journal of Differential Equations, 2021(40), pp. 1-13.
Rights
Attribution 4.0 International