Coexistence States for a Non-Cooperative Model Arising in Reactor Dynamics with Heat Exchange

The existence of coexistence states of a non-cooperative nuclear reactor model is investigated in this paper. Differently from the existing literature, we allow the nonlinearities to not necessarily be linearizable at zero and infinity, and the boundary condition in the model implies that the nuclear reactor has heat exchange with the external environment, which much more closely reflects the situation in reality. Several novel existence theorems distinct from existing results in the literature are established by means of bifurcation theory. Our main findings will not only be helpful to enrich the related theories of nuclear reactor models but also have certain guiding significance for the safe operation of reactors.