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In this paper we deal with existence and uniqueness of solution tosuper-linear problems for the Pucci operator: $$ -\M^+(D^2u)+|u|^{s-1}u=f(x)\quad {in} \RR^n, $$ where $s>1$ and $f$ satisfies only local integrabilityconditions. This result is well known when, instead of the Pucci operator, theLaplacian or a divergence form operator is considered. Our existence resultsuse the Alexandroff-Bakelman-Pucci inequality since we cannot use anyvariational formulation. For radially symmetric $f$ we can prove our resultsunder less local integrability assumptions, taking advantage of an appropriatevariational formulation. We also obtain an existence result with boundaryexplosion in smooth domains.

Super-linear elliptic equation for the Pucci operator without growth restrictions for the data