This is an interesting survey on the nonlinear eigenvalue problem , with being a 1-homogeneous continuous operator which leaves a cone in a Banach space invariant. Particular emphasis is put on compact or, more generally, condensing operators (w.r.t. a suitable measure of noncompactness). Applications are given to operators of the form
in spaces of continuous functions ; here and are continuous on with , while is continuous and nonnegative on . In particular, the authors compare the spectral radii
and give conditions under which these numbers coincide. It seems that they are unaware of contributions by M. Martelli [Ann. Mat. Pura Appl., IV. Ser. 145, 1-32 (1986; Zbl 0618.47052)] and G. Fournier and M. Martelli [Topol. Methods Nonlinear Anal. 2, No. 2, 203-224 (1993; Zbl 0812.47059)] to this field.