Entire solutions of sublinear elliptic equations in anisotropic media

We study the nonlinear elliptic problem -Delta u = rho(x)f(u) in R-N (N >= 3), lim(vertical bar x vertical bar ->infinity) u(x) = l, where l >= 0 is a real number, rho(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 p(x) decays fast enough at infinity. Our arguments rely on comparison techniques and on a theorem of Brezis and Oswald for sublinear elliptic equations. (c) 2005 Elsevier Inc. All rights reserved.