Applications of monotone operators to a class of semilinear elliptic BVPs in unbounded domain

We study the existence of a weak solution for a semilinear elliptic Dirichlet boundary-value problem Lu(x) - mu ug(1) (x) + h(u)g(2)(x) = f (x) in Omega, u(x) = 0 on partial derivative Omega, in a suitable weighted Sobolev space, where Omega = R-n\K,n >= 3 is an unbounded domain, and where K is a closure of some bounded domain in R-n, n >= 3.