Entire solutions of sublinear elliptic equations in anisotropic media

We study the nonlinear elliptic problem −Δu=ρ(x)f(u) in RN (N⩾3), lim|x|→∞u(x)=ℓ, where ℓ⩾0 is a real number, ρ(x) is a nonnegative potential belonging to a certain Kato class, and f(u) has a sublinear growth. We distinguish the cases ℓ>0 and ℓ=0 and prove existence and uniqueness results if the potential ρ(x) decays fast enough at infinity. Our arguments rely on comparison techniques and on a theorem of Brezis and Oswald for sublinear elliptic equations.