Maximum principles and nonexistence results for radial solutions to equations involving p‐Laplacian

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.