Entire solutions of sublinear elliptic equations in anisotropic media

We study the nonlinear elliptic problem $-\mathrm{\Delta }u=\rho (x)f(u)$ in ${\text{RR}}^N$ ($N\ge 3$), $\lim \mathrm{\_}\mathrm{\mid }x\mathrm{\mid }\text{ri}\mathrm{\infty }u(x)=\mathrm{\ell }$, where $\mathrm{\ell }\ge 0$ 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 $\mathrm{\ell }>0$ and $\mathrm{\ell }=0$ and we prove existence and uniqueness results if the potential $\rho (x)$ decays fast enough at infinity. Our arguments rely on comparison techniques and on a theorem of Brezis and Oswald for sublinear elliptic equations.