Abstract

We establish the existence of at least one nonnegative solution for the problem(P) ?-div(a(|?u|)?u)=?f(u)in?,u= 0on??,where a and f satisfy conditions near zero. Here the novelty is that we do not need restrictions on the nonlinearities at infinity. Therefore, we can consider subcritical, critical and supercritical cases. © 2003 Elsevier Ltd. All rights reserved.