Sublinear elliptic eigenvalue problems in ${R}\sp n$

In this paper we study a nonlinear elliptic equation in all $\rn$. Using topological methods (bifurcation theory), we prove the existence of a branch (i.e. a closed connected subset) of nontrivial nonnegative solutions of the problem. In the last section we investigate some connections between our results and an existence condition introduced by H. Brezis and S. Kamin in \cite{BK}. We show that this condition affects the behaviour of the branch of positive solutions.