Thispaperisconcernedwiththeharmonicequation(P_(■ε)):?u=0,u>0inB~nand?u/?ν+((n-2)/2)u=((n-2)/2)Ku~(n/(n-2)■ε)onS~(n-1)whereB~nistheunitballinR~n,n≥4withEuclideanmetricg_0,?B~n=S~(n-1)isitsboundary,KisafunctiononS~(n-1)andεisasmallpositiveparameter.Weconstructsolutionsofthesubcriticalequation(P_(-ε))whichblowupatonecriticalpointofK.WegivealsoasufficientconditiononthefunctionKtoensurethenonexistenceofsolutionsfor(P_(-ε))whichblowupatonepoint.Finally,weproveanonexistenceresultofsinglepeakedsolutionsforthesupercriticalequation(P_(+ε)).
