Asymptotic bechaviour of the solutions of sublinear elliptic equations with a potential

Abstract

We study the limit behaviour of nonnegativesolutions of the semilinear elliptic equation with a sublinear nonlinearity and a potential

where and . The estimates lie upon a mean value inequality for the Helmoltz operator is cast c>0. The behaviour of the solutions is essentially anisotropic, with possible dead cores.