Maximum principles and nonexistence results for radial solutions to equations involvingp-Laplacian

Abstract

We obtain the variant of maximum principle for radial solutions of, possibly singular, p-harmonic equations of the form as well as for solutions of the related ODE. We show that for the considered class of equations local maxima of |w| form a monotone sequence in |x| and constant sign solutions are monotone. The results are applied to nonexistence and nonlinear eigenvalue problems. We generalize our previous work for the case h≡0. Copyright © 2010 John Wiley & Sons, Ltd.