Entire solutions of sublinear elliptic equations in anisotropic media

We study the nonlinear elliptic problem −∆u = ρ(x)f(u) in R (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 we 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. 2000 Mathematics Subject Classification: 35B40, 35B50, 35J60, 58J05.