Existence of Radial Solutions for Quasilinear Elliptic Equations with Singular Nonlinearities

Beatrice Acciaio and Patrizia Pucci


We prove the existence of radial solutions of the quasilinear elliptic equation div(A(|Du|)Du) + f(u) = 0 in R^n, n > 1, where f is either negative or positive for small u > 0, possibly singular at u = 0, and grows subcritically for large u. Our proofs use only elementary arguments based on a variational identity. No differentiability assumptions are made on f.