简介：在这篇论文，由固定的点索引理论，为线性的潜水艇和经由二的asymptotically线性的操作员的固定的点的号码联合了平行亚super答案被学习。在合适的条件下面，为线性的潜水艇和asymptotically线性的操作员的至少九或七个不同的固定的点的存在被证明。最后，理论结果被用于Hammerstein不可分的方程的一个非线性的系统。

简介：Thewaveequationwithvariablecoefficientswithanonlineardissipativeboundaryfeedbackisstudied.BytheRiemanniangeometrymethodandthemultipliertechnique,itisshownthattheclosedloopsystemdecaysexponentiallyorasymptotically,andhencetherelationbetweenthedecayrateofthesystemenergyandthenonlinearitybehaviorofthefeedbackfunctionisestablished.

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简介：AD(Alternatingdirection)Galerkinschemesford-dimensionalnonlinearpseudo-hyperbolicequationsarestudied.Byusingpatchapproximationtechnique,ADprocedureisrealized,andcalculation,workissimplified.ByusingGalerkinapproach,highlycomputationalaccuracyiskept.Byusingvariousprioriestimatetechniquesfordifferentialequations,difficultycomingformnon-linearityistreated,andoptimalH^1andL^2convergenceprop-ertiesaredemonstrated.Moreover,althoughalltheexistedADGalerkinschemesusingpatchapproximationarelimitedtohaveonlyoneorderaccuracyintimeincrement,yettheschemesformulatedinthispaperhavesecondorderaccuracyinit.ThisimpliesanessentialadvancementinADGalerkinaualysis.

简介：这份报纸与推迟的中子和一般边界条件处理一个非线性的运输方程。我们建立，经由Lp-spaces(1p<+)。本地、非本地的进化问题被讨论。

简介：InthispaperweanalyzetheoptimalcontrolproblemforaclassofaffinenonlinearsystemsundertheassumptionthattheassociatedLiealgebraisnilpotent.TheLiebracketsgeneratedbythevectorfieldswhichdefinethenonlinearsystemrepresentaremarkablemathematicalinstrumentforthecontrolofaffinesystems.Wedeterminetheoptimalcontrolwhichcorrespondstothenilpotentoperatorofthefirstorder.Inparticular,weobtainthecontrolthatminimizestheenergyofthegivennonlinearsystem.Applicationsofthiscontroltobilinearsystemswithfirstordernilpotentoperatorareconsidered.

简介：ThedynamicalcharacterforaperturbedcouplednonlinearSchrodingersystemwithperiodicboundaryconditionwasstudied.First,thedynamicalcharacterofperturbedandunperturbedsystemsontheinvariantplanewasanalyzedbythespectrumofthelinearoperator.Thentheexistenceofthelocallyinvariantmanifoldswasprovedbythesingularperturbationtheoryandthefixed-pointargument.

简介：Oneofthemostinterestingproblemsofnonlineardifferentialequationsistheconstructionofpartialsolutions.Anewmethodispresentedinthispapertoseekspecialsolutionsofnonlineardiffusionequations.ThismethodisbasedonseekingsuitablefunctiontosatisfyBernolliequation.Manynewspecialsolutionsareobtained.

简介：Thispaperproposesasortofnewnormalformsconsistingofobserverformandcontrollableformfornonlinearsystems.Theconditionsfortransformingtothesenormalformsaregiven,respectively.Thesenormalformsareusedtotreattheproblemsofobserverdesignandlinearization.Thefirstpartofthispaperdealswiththeobserverform,andthesecondthecontrollableform.

简介：Existenceofsolutionsforsemiboundednonlinearevolutionequationsisestablished.Thisgivesmoreaccurateestimateofsolutionsandconditionsofexistenceaxemoreeasilyvalidated.OurresultsaresuccessfullyappliedtoproveexistenceanduniquenessofsolutionsforsomeKdVtypeequations.

简介：Inthispaper,weinvestigatethesemiclassicallimitofthegeneralizednonlinearSchr?dingerequationforinitialdatawithSobolevregularity.Also,wewillanalyzethestructureofthefluiddynamicalsystemwithquantumeffectcorrespondingtothesemiclassicallimitofthegeneralizednonlinearSchr?dingerequation.

简介：Volterraseriesisapowerfulmathematicaltoolfornonlinearsystemanalysis,andthereisawiderangeofnonlinearengineeringsystemsandstructuresthatcanberepresentedbyaVolterraseriesmodel.Inthepresentstudy,therandomvibrationofnonlinearsystemsisinvestigatedusingVolterraseries.Analyticalexpressionswerederivedforthecalculationoftheoutputpowerspectraldensity（PSD）andinput-outputcross-PSDfornonlinearsystemssubjectedtoGaussianexcitation.Basedontheseexpressions,itwasrevealedthatboththeoutputPSDandtheinput-outputcrossPSDcanbeexpressedaspolynomialfunctionsofthenonlinearcharacteristicparametersortheinputintensity.Numericalstudieswerecarriedouttoverifythetheoreticalanalysisresultandtodemonstratetheeffectivenessofthederivedrelationship.TheresultsreachedinthisstudyareofsignificancetotheanalysisanddesignofthenonlinearengineeringsystemsandstructureswhichcanberepresentedbyaVolterraseriesmodel.

简介：NonlinearMHDKelvin-Helmholtz（K-H）instabilityinapipeistreatedwiththederiva-tiveexpansionmethodinthepresentpaperThelinearstabilityproblemwasdiscussedinthepastbyChandrasekhar（1961）andXuetal.（1981）.Nagano（1979）discussedthenonlinearMHDK-Hinstabilitywithinfinitedepth.Heusedthesingularperturbationmethodandextrapolatedtheob-tainedsecondordermodifierofamplitudevs.frequencytoseekthenonlineareffectontheinstabilitygrowthrateγ.However,inourview,suchanextrapolationisinappropriate.Becausewhentheinstabili-tysetsin,thegrowthratesofhigher,ordertermsontherighthandsideofequationswillexceedthecor-respondingsecularproducingterms,sotheexpansionwillstillbecomemeaninglessevenifthesecularproducingtermsareeliminated.Mathematicallyspeaking,it’simpossibletoderiveformula（39）whenγ02isnegativeinNagano’spaper.Moreover,evenasearlyasγ02→O+,theexpansionbe-comesinvalidbecausethe2ndordermodifierγ2（inhisformula（56））tendstoinfinity.Thisweak-nessisremovedinthispaper,andtheresultisextendedtothecaseofapipewithfinitedepth.

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简介：我们由使用量基因算法(QGA)和HartreeFockRoothaan(HFR)的联合计算精力特征值和一个电子量点(QD)的sate功能方法。线性并且为1s-1p，1p-1d，和1d-1f转变的第三顺序的非线性的光吸收系数为stoichiometric比率的三不同的值作为事件光子精力的一个函数被检验。结果证明stoichiometric比率，杂质，松驰时间，和点尺寸在QD的光吸收系数上有大影响。

简介：Inthispaper,amodifiednonlineardynamicinequalityontimescalesisusedtostudytheboundednessofaclassofnonlinearthird-orderdynamicequationsontimescales.Thesetheoremscontainasspecialcasesresultsfordynamicdifferentialequations,differenceequationsandq-differenceequations.

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