On the existence of positive solutions of nonlinear elliptic equations

We study the existence of positive solutions of the nonlinear elliptic prob lem 1/2 Deltau - f(u) . mu + g(u) . sigma = 0 in D with u = 0 on partial de rivativeD, where mu and sigma are two Randon's measures belonging to a Kato subclass and D is an unbounded smouth domain in R-d(d greater than or equa l to 3). When g is superlinear at 0 and 0 less than or equal to f(t) less t han or equal to t for t is an element of (0,b), then probabilistic methods and fixed point argument are used to prove the existence of infinitely many bounded continuous solutions of this problem.