The effect of a temperature-dependent feedback on the behavior of a nuclear reactor was studied in several papers [IA] by using the time-dependent diffusion approximation. Feedback was assumed to act only through the multiplication factor. In the papers of Belleni-Morante and co-workers [5-81, the time evolution of a reactor was studied taking into account temperature-dependent cross sections, multiplication factors, and energy generation coefficients. Delayed neutrons were considered in [7], whereas, in [6, 81, the coupling between neutron density and temperature was given by the heat diffusion equation. The techniques employed rely on the theory of semigroups of operators in Banach spaces. The problem of the possibility of a stationary nontrivial solution remained open, and our aim in this work is to investigate such a possibility. For simplicity, we consider a homogeneous slab with macroscopic cross section and multiplication factor depending upon temperature, and we assume that the coupling between neutron population and temperature is represented by a “conservation” equation simpler than the heat diffusion equation. Moreover, we disregard delayed neutrons because they would imply one more equation of a similar type. The problem is set out in the framework of the theory of cones in Banach spaces and of positive operators. We introduce two real Banach spaces X,, = L1([--a, a] x [-1, I]) x