Weak solutions for a class of semilinear elliptic equations in unbounded domains of R~3

摘要

We study the existence of a weak solution for a semilinear elliptic Dirichlet boundary-value problem Lu(x)+∑(g_i(x)h_i(u(x))D_iu(x)=f(x))(1≤i<3), x∈Ω, u=0, x∈ {partial deriv}Ω, in a suitable weighted Sobolev space, where Ω=R~3K is an unbounded domain, and where K is a closure of some bounded domain in R~3.