Weak solutions for degenerate semilinear elliptic BVPs in unbounded domains

In this article, we prove the existence of a weak solution for the degenerate semilinear elliptic Dirichlet boundary-value problem $$displaylines{ Lu(x)+sum_{i=1}^n g(x)h(u(x))D_iu(x)=f(x)quad hbox{in }Omega,cr u=0quad hbox{on }partialOmega, }$$ in a suitable weighted Sobolev space. Here $Omegasubsetmathbb{R}^n$, $1leq nleq3,$ is not necessarily bounded.