Super-linear Elliptic Equation for the Pucci Operator without Growth Restrictions for the Data

In this paper we deal with existence and uniqueness of solution to super-linear problems for the Pucci operator: −M(Du) + |u|u = f(x) in IR, where s > 1 and f satisfies only local integrability conditions. This result is well known when, instead of the Pucci operator, the Laplacian or a divergence form operator is considered. Our existence results use the Alexandroff-Bakelman-Pucci inequality since we cannot use any variational formulation. For radially symmetric f we can prove our results under less local integrability assumptions, taking advantage of an appropriate variational formulation. We also obtain an existence result with boundary explosion in smooth domains.