LOCALIZED RADIAL SOLUTIONS FOR A NONLINEAR P-LAPLACIAN EQUATION IN RN

Abstract. We establish the existence of radial solutions to the p-Laplacian equation ∆pu+f(u) = 0 in RN, where f behaves like |u|q−1u when u is large and f(u) < 0 for small positive u. We show that for each nonnegative integer n, there is a localized solution u which has exactly n zeros. 1