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 -a(vertical bar x vertical bar)Delta(p()w) + h (vertical bar x vertical bar, w, del w(x) . x/vertical bar x vertical bar) = phi(w), as well as for solutions of the related ODE. We show that for the considered class of equations local maxima of vertical bar w vertical bar form a monotone sequence in vertical bar x vertical bar 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 equivalent to 0. Copyright (C) 2010 John Wiley & Sons, Ltd.