Thispaperdealswiththesolutionofaneutrontransportequationwithparameterδ.Usingthetheoryoffunctionalanalysis,wediscussthedistributionoftheparameterswhichmaketheequationhaveanon-zerosolution,andobtainanecessaryandsufficientconditionfortheexistenceofthecontrolcriticaleigenvalueδ0whichpossessesaphysicalmeaning.