Wang, Wei-Chuan2021-08-262021-08-262021-05-07Wang, W. C. (2021). Existence of sign-changing solutions for radially symmetric p-Laplacian equations with various potentials. <i>Electronic Journal of Differential Equations, 2021</i>(40), pp. 1-13.1072-6691https://hdl.handle.net/10877/14450In 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.Text13 pages1 file (.pdf)enAttribution 4.0 InternationalNonlinear p-Laplacian equationSign-changing solutionBlow-up solutionArticle