Résumé en anglais

We deal with existence and uniqueness of the solution to the fully nonlinear equation−F(D2u)+ |u|s−1u = f(x)in Rn,where s> 1 and f satisfies only local integrability conditions. This result is well known when, instead ofthe fully nonlinear elliptic operator F, the Laplacian or a divergence-form operator is considered. Ourexistence results use the Alexandroff–Bakelman–Pucci inequality since we cannot use any variationalformulation. For radially symmetric f, and in the particular case where F is a maximal Pucci operator,we can prove our results under fewer integrability assumptions, taking advantage of an appropriatevariational formulation. We also obtain an existence result with boundary blow-up in smooth domains.