Steady states of a non-cooperative model arising in nuclear engineering

Abstract

This paper studies the existence and the uniqueness of coexistence states in a spatially heterogeneous reaction diffusion model originated by the theory of nuclear reactors. The mathematical relevance of our analysis relies on the fact that the underlying variational systems are of non-cooperative type and, consequently, the nice comparison techniques available for cooperative systems fail to be true, making the problem of ascertaining whether or not the model admits a unique coexistence state an extremely challenging task. In this paper we are giving a series of new uniqueness results complementing those available in the literature.