Existence of the first eigenvalue for the problem of \(P_ 1\)- approximation of a kinetic equation (Q1080085)

The paper deals with an operator equation determined by a spectral problem in reactor theory. It reduces to a linear problem of the form: \(Au=\mu u\), where \(A=R+Q\) acts on the direct sum of a finite number of copies of \(L^ 2(V)\), V being a domain in \(R^ n\) of finite measure and \(n\leq 3\). The main result gives sufficiency condition for the operator A to have a simple positive eigenvalue with the corresponding eigenvector satisfying a positivity condition.