简介：Inthispaperweproveanonvariationalformofarain-maxproblemin[l]andgiveitsapplicationtoaperiodicalproblem.

简介：<正>WeareconcernedwiththefollowingDirichletproblem:-△u（x）=f（x,u）,x∈Ω.u∈H01（Ω）.（P）wheref（x,t）∈C（Ω×R）,f（x,t）/tisnondecreasingint∈RandtendstoanL∝-functionq（x）uniformlyinx∈Ωast→+∝（i.e.,f（x,t）isasymptoticallylinearintatinfinity）.Inthiscase.anAmbrosetti-Rabinowitz-typecondition,thatis.forsomeθ>2.M>0,0<θF（x.s）≤f（x,s）s,forall|s|≥Mandx∈Ω,（AR）isnolongertrue,whereF（x,s）=integralfromn=0tosf（x,t）dt.Asiswellknown,（AR）isanimportanttechnicalconditioninapplyingMountainPassTheorem.Inthispaper,withoutassuming（AR）weprove,byusingavariantversionofMountainPassTheorem,thatproblem（P）hasapositivesolutionundersuitable,conditionsonf（x,t）andq（x）.Ourmethodsalsoworkforthecasewheref（x,f）issuperlinearintatinfinity.i.e.,q（x）≡∞.

简介：AssumethatBisacompactsubsetontherealaxiscontainingatleastn+1points,C（B）thenormedlinearspaceofallcontinuousfunctionsdefinedonB,withChebyshevnorm‖·‖,andG=span（g1,…,gn）ann-dimensionalsubspaceofC（B）.LetGR={g=sumfromj=1tonajgj:v（x）≤g（x）≤u（x）,qi≤sumfromj=1tondijaj≤pifori=1,…,l}whereu,vareextendedreal-valuedfunctionsonBsubjectto-∞≤v（x）

简介：In1972,Fullerprovedthatacompleteadditivesubeategory_RCofR-Modisequivalenttoamodulecategory⊿-Modifandonlyif_RC=Gen(_RU)forsomequasiprogenerator_RUand⊿≌End_RUcanonically.Inthisnotetheauthorgivesacharacterizationof_RCwhichmakes_RUaprojectiveR-moduleinthecasewhenRisarightperfectringwithidentity,andshowsthatR-ModistheuniquecompleteadditivesubcategoryofR-ModwhichisequivalenttoR-ModforaleftArtinianringR.

简介：Aboundoduesscriterionissetup/orsomeconvolutionoperatorsonacompaotLiegroup,BythiscriterionaHoermandermultipliertheoremisprovedintheHardyspacesonSU(2).

简介：InthispaperwepresentacorrectionoftheproofofustronguniquenesstheoremgivenbyH.Struuss[1]in1992onapproximationbyreciprocalsoffunctionsufann-dimensionalspace(u,…un)satisfyingcoefficientconstraints.

简介：Apicardtypetheoremisproved,andacounterexampleisgiventoshowthattheBlochLawisnottruegenerally.

简介：<正>Inthispaper,weinvestigatethegeneralizedSublaplacian.Wegivetheexpressionoftherestrictionoperatorsexplicitly.Byintroducingthegeneralizedλ-twistedconvolutions,weobtaintheestimatesoftherestrictionoperatorsinthemixedL~Pspaces.Finally,wegetarestrictiontheoremassociatedwiththegeneralizedSublaplacian.

简介：InthispaperwepresentacorrectionoftheproofofastronguniquenesstheoremgivenbyH.Straussin1992onapproximationbyreciprocalsoffunctionsofann-dimensionalspacespan（u1,…,un）satisfyingcoefficientconstraints.

简介：Aseveryoneknows,theclassicalJacksontheoreminapproximationtheorywasgeneralizedinLpspacesbyR.A.Devore.Inthispaper,weprovedtheJacksontheoreminB,spaceswhichintroducedbyDingXiaXi,

简介：SupposethatEandFareseparableBanachspaces,XandYareindependentsymmetricEandF-valuedrandomvectorsrespectively.ThispaperisdevotedtothestudyofthecentrallimittheoremforX（○×）YintheinjoctiveandprojectivetensorproductspacesE（∨○×）FandE（∧○×）F.Specialattentionispaidtoι2（∧○×）ι2.Inaddition,twocounter-examplesaregiven.

简介：Thedistortiontheoremforbiholomorphicstarlikemappings(withrespecttoorigin)inboundedsymmetricdomainsaregiven,Thedistortiontheoremforlocallybiholomorphicconvexmappingsinboundedsymmetricdomainsaregivenalso.

简介：Withthehelpofalimitpropertyofsolutionsofbackwardstochasticdifferentialequations(BSDEs),thispaperestablishesaconversecomparisontheoremfordeterministicgeneratorsgofBSDEsundertheassumptiong(t,y,0)≡0.

简介：ＯＮＡＦＩＮＩＴＥＮＥＳＳＴＨＥＯＲＥＭＡＢＯＵＴＰＲＯＢＬＥＭＳＩＮＶＯＬＶＩＮＧＩＮＥＱＵＡＬＩＴＩＥＳ￥ＷＵＷｅｎｉｎｎ（ＷＵＷｅｎ－ｔｓｕｎ）（ＩｎｓｔｉｔｕｔｅｏｆＳｙｓｔｅｍｓＳｃｉｅｎｃｅ，ＡｃａｄｅｍｉａＳｉｎｉｃａ，Ｂｅｉｊｉｎｇ１...

简介：Basedon[1],thispapergivesconcreteestimatesfordistortiontheoremforbiholomorphicconvexmappingsinclassicaldomainsoftypesⅠ,Ⅱ,andⅢincludingtransitivedomainswhichareholomorphicallyhomeomorphictothesedomains.

简介：Inthepresentpaperatheoremisestablishedwhichofferssomenecessaryandsufficienteonditionsforahexagonalsystemtohaveperfectmatchings.

简介：Thispaperpresentsthestabilityofdifferenceapproximationsofanoptimalcontrolproblemforaquasilinearparabolicequationwithcontrolsinthecoefficients,boundaryconditionsandadditionalrestrictions.Theoptimalcontrolproblemhasbeenconveredtooneoftheoptimizationproblemusingapenaltyfunctiontechnique.Thedifferenceapproximationsproblemfortheconsideredproblemisobtained.Theestimationsofstabilityofthesolutionofdifferenceapproximationsproblemareproved.Thestabilityestimationofthesolutionofdifferenceapproximationsproblembythecontrolsisobtained.

简介：

简介：Thispaperproposesaformallystrongerset-valuedClaxke'sfixedpointtheorem.Bythis-theoremwecanimproveafixedpointtheoremforweaklyinwardcontractionset-valuedmappingofD.DowingandW.A.Kirk.

简介：AradialfunctioncanbeexpressedbyitsgeneratorthroughThepositivedefiniteofthefunctionplaysanimportantroteintheradialbasisinterpolation.WecannaturallyuseBochner’sTheoremtocheckifispositivedefinite.Thisrequireshoweveran-dhnensiotialFouriertransformationanditisnotveryeasytocalculate.Furthermoreinalotofcaseswewilluseforspacesofvariousdimensionstoo,thenforeveryfixednweneeddotheFouriertransformationoncetocheckifthefunctionispositivedefiniteinthen-di-mensionalspace.Thecompletelymonotonefunction:,whichisdiscussedin[4]ispositivedefiniteforarbitraryspacedimensions.Withthistechniquetvecanveryeasilycharacterizethepositivedefinite,ofaradialfunctionthroughitsgenerator.Unfortunatelythereisonlyaverysmallsubsetofradialfunctionwhichiscompletelymonotone.Thusthiscriterionexcludedalotofinterestingfunctionssuchascompactlysupportedradialfunction,whcihareveryusefulinapplic