Abstract
We study the existence of positive solutions of the nonlinear elliptic equation Deltau + phi((.), u) = 0, in an unbounded domain D in R-n, n greater than or equal to 3, with compact boundary. Our purpose is to give some existence results for the above equation with some boundary values, where the nonlinear term phi(t,x) satisfies some appropriate conditions related to a certain Kato class K-infinity(D). We give also some estimates on the solution u.