简介:<正>Inthispaperweconsiderasemi-dicretizednonlinearSchrdinger(NLS)equationwithlocalintegralnonlinearity.Itisprovedthatforeachmeshsize,thereexistattractorsforthediscretizedsystem.TheboundstortheHausdorffandfractaldimensionsofthediscreteattractorsareobtained,andthevariousboundsareindependentofthemeshsizes.Furthermore.numericalexperimentsaregivenandmanyinterestingphenomenaareobservedsuchaslimitcycles,chaoticattractorsandaso-calledcrisisofthechaoticattractors.
简介:Afewweakandstrongconvergencetheoremsofthemodifiedthree-stepiterativesequencewitherrorsandthemodifiedIshikawaiterativesequencewitherrorsforasymptoticallynon-expansivemappingsinanynon-emptyclosedconvexsubsetsofuniformlyconvexBanachspacesareestablished.TheresultspresentedinthispapersubstantiallyextendtheresultsduetoChang(2001),Osilikeandhniagbosor(2000),Rhoades(1994)andSchu(1991).
简介:Inthispaper,thebehaviorforcommutatorsofaclassofbilinearsingularintegraloperatorsassociatedwithnon-smoothkernelsontheproductofweightedLebesguespacesisconsidered.BysomenewmaximalfunctionstocontrolthecommutatorsofbilinearsingularintegraloperatorsandCMO(Rn)functions,compactnessforthecommutatorsisproved.
简介:Inthisarticle,wewillinvestigatethepropertiesofiterativesequencefornon-expansivemappingsandpresentseveralstrongandweakconvergenceresultsofsuccessiveapproximationstofixedpointsofnon-expansivemappingsinuniformlyconvexBanachspaces.Theresultspresentedinthisarticlegeneralizeandimprovevariousonesconcernedwithconstructivetechniquesforthefixedpointsofnon-expansivemappings.
简介:Inthisarticle,byusingtheoryoflinearevolutionsystemandSchauderfixedpointtheorem,weestablishasufficientresultofexactnullcontrollabilityforanonautonomousfunctionalevolutionsystemwithnonlocalconditions.Inparticular,thecompactnesscondi-tionorLipschitzconditionforthefunctionginthenonlocalconditionsappearinginvariousliteraturesisnotrequiredhere.Anexampleisalsoprovidedtoshowanapplicationoftheobtainedresult.
简介:Inthisarticle,weobtaintheL~p-boundednessofcommutatorsofLipschitzfunctionsandsingularintegralswithnon-smoothkernelsonEuclideanspaces.
简介:Westudytheexistenceoftravelingwavesolutionsforanonlocalandnon-monotonedelayedreaction-difusionequation.Basedontheconstructionoftwoassociatedauxiliaryreactiondifusionequationswithmonotonicityandbyusingthetravelingwavefrontsoftheauxiliaryequations,theexistenceofthepositivetravelingwavesolutionsforc≥cisobtained.Also,theexponentialasymptoticbehaviorinthenegativeinfnitywasestablished.Moreover,weapplyourresultstosomereactiondifusionequationswithspatio-temporaldelaytoobtaintheexistenceoftravelingwaves.Theseresultscover,complementand/orimprovesomeexistingonesintheliterature.
简介:Inthispaper,weareconcernedwiththeexistenceofperiodicsolutionsofsecond-ordernon-autonomoussystems.ByapplyingtheSchauder'sfixedpointtheoremandMiranda'stheorem,anewexistenceresultofperiodicsolutionsisestablished.
简介:AclassofnonlinearparabolicequationonapolygonaldomainΩR2isinves-tigatedinthispaper.Weintroduceafiniteelementmethodonoverlappingnon-matchinggridsforthenonlinearparabolicequationbasedonthepartitionofunitymethod.Wegivetheconstructionandconvergenceanalysisforthesemi-discreteandthefullydiscretefiniteelementmethods.Moreover,weprovethattheerrorofthediscretevariationalproblemhasgoodapproximationproperties.Ourresultsarevalidforanyspatialdimensions.Anumericalexampletoillustratethetheoreticalresultsisalsogiven.
简介:在这篇文章,我们得到non-selfsimilar基本在另一种看法能量守恒定律飘动,它与平常的自我类似的转变不同。答案有不同全球结构。这篇文章被划分成三部分。第一部分是介绍。在第二部分,我们讨论non-selfsimilar基本波浪和他们二维的能量守恒定律的一个班的相互作用。在这种情况中,我们考虑起始的断绝是有u+的抛物线的盒子>0,当明确的non-selfsimilar变成稀薄波浪能被获得时。在第二部分,我们考虑盒子u+的答案结构<0。新答案结构被在不同基本波浪之间的相互作用获得,并且将继续与另外的状态交往。全球答案将与一种尺寸的状况很不同。
简介:AccordingtotheanalyticalcharacteristicsofcubicBsplinefunction,suchascompactnessanddiscontinuoussmoothness,twomethods,GlobalintegralmethodandAssemblingmethodareproposedtocalculatethenon-linearstiffnessmatrixinthesplinefiniteelementmethod.TheGlobalintegralmethodtransformstheintegraloftheproductofsplinefunctionsintothesumofboundarydataoftheproductbyintegralbyparts.TheAssemblingmethodusesthecompactnesscharacteristicsofthesplinefunction,reducesthen+3orderstiffnessmatrixinunitintervaltothe4ordermatrix,andthenobtainstheglobalmatrixbyassemblingthesmallones.Thetwoproposedmethodsareclearintheoryandeasytoberealizedbycomputerprogram,whichcaneffectivelyimprovetheefficiencyofthealgorithmfornonlinearsplineelementmethod.
简介:1.IntroductionTherearealotofresultsaboutHammersteinintegralequations(see[1]),butsupen-linearproblemsaredifficult;thereareonlyafewresultsaboutit.In[2,3]theauthorsstudysuperliniearintegralequations;in[4]theauthorsstudysystemofsuperlinearintegralequatio...
简介:Nonlineardynamicalsystemsaresometimesundertheinfluenceofrandomfluctuations.Itisdesirabletoexaminepossiblebifurcationsforstochasticdynamicalsystemswhenaparametervaries.Acomputationalanalysisisconductedtoinvestigatebifurcationsofasimpledynamicalsystemundernon-Gaussianα-stableLévymotions,byexaminingthechangesinstationaryprobabilitydensityfunctionsforthesolutionorbitsofthisstochasticsystem.ThestationaryprobabilitydensityfunctionsareobtainedbysolvinganonlocalFokker-Planckequationnumerically.Thisallowsnumericallyinvestigatingphenomenologicalbifurcation,orP-bifurcation,forstochasticdifferentialequationswithnon-GaussianLévynoises.