EXISTENCE OF SIGN-CHANGING SOLUTIONS FOR RADIALLY SYMMETRIC p-LAPLACIAN EQUATIONS WITH VARIOUS POTENTIALS

In this article, we study the nonlinear equation (r(n-1)vertical bar u'(r)vertical bar(p-2)u'(r))' + r(n-1) w(r)vertical bar u(r)vertical bar(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, Prufer-type substitutions, and some integrals involving the p-Laplacian.