and

We show existence and regularity of solutions in RN to nonlinear elliptic equations of the form −divA(x,Du) + g(x, u) = f, when f is just a locally integrable function, under appropriate growth conditions on A and g but not on f. Roughly speaking, in the model case −∆p(u) + |u|s−1u = f, with p> 2 − (1/N), existence of a nonnegative solution in RN is guaranteed for every nonnegative f ∈ L1loc(RN) if and only if s> p − 1. AMS Classification: 35J60, 35J70