Abstract
The article considers steady-state solutions for multigroup neutron transport systems. Neutron density is divided into N energy groups in an m-dimensional convex bounded domain, $m\geqq 1$. Conditions for nonexistence (unboundedness) as well as for existence of bounded solutions are found. The methodinvolves the use of upper and lower solutions for the systems of integral transport equations. An interesting and important result concerning the positivity of related principal eigenfunction for the integral equation is obtained. It is used in the proof of the nonexistence case by means of a sweeping procedure. For the existence case, an upper solution is first constructed and then a monotone sequence converging to the solution of the system is iteratively constructed. The result is then applied to determine criteria on the size of the transport region and the transfer and scattering cross sections, so that the system with a given source and boundary condition does or does not have any nonnegative bounded solution.
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