Summary: We establish results concerning non-existence and existence of entire positive solutions for the nonlinear elliptic problem
where with ; , are locally Hölder continuous functions and is a real parameter. The main purpose of this paper, in short, is to complement the principal theorem of B. Xu and Z. Yang [Bound. Value Probl. 2007, Article ID 16407, 8 p. (2007; Zbl 1139.35348)] showing existence and non-existence of solutions for the above problem for appropriately.