ThisarticledealswiththedegenerateparabolicequationsinexteriordomainsandwithinhomogeneousDirichletboundaryconditions.Weobtainthatpc=(σ+m)n/(n-σ-2)isitscriticalexponentprovidedmax{-1,[(1-m)n-2]/(n+1)}<σpc,theequationsadmitglobalpositivesolutionsforsomeboundaryvaluesandinitialdata.Meantime,wealsodemonstratethatitspositivesolutionsblowupinfinitetimeprovidedn≤σ+2.
