NONLINEAR ELLIPTIC-EQUATIONS IN R(N) WITHOUT GROWTH RESTRICTIONS ON THE DATA

We show existence and regularity of solutions in RN to nonlinear elliptic equations of the form -div A(x, Du) + g(x, u) = f(hook) when f(hook) is just a locally integrable function, under appropriate growth conditions on A and g but not on f(hook). Roughly speaking, in the model case -Δp(u) + |u|s-1u = f(hook) with p > 2 - (1/N), existence of a nonnegative solution in RN is guaranteed for every nonnegative f(hook) ∈ L1loc(RN) if and only if s > p - 1. © 1993 by Academic Press, Inc.