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简介：Inthisarticle,theauthorsstudysomebasicpropertiesoftheso-calledquasilinearadditivefunctions,andsomeapplicationstothespecialfunctionsofquasiconformalanalysisarespecified.

简介：Theexistenceanduniquenessresultsaboutquasilinearperiodicboundaryvalueproblemsareestablishedbyusingtheglobalinversefunctiontheoremandtheresultabouttheexistenceanduniquencessofperiodicsolutionsfortheperiodicboundaryvalueproblemofnonhomogeneouslinearperiodicsystem.

简介：Inthispaper,usingcapacitytheoryandextensiontheoremofLipschitzfunctionswefirstdiscusstheuniquenessofweaksolutionofnonhomogeneousquasilinearellipticequationsinspaceW(θ,p)(Ω),whichisbiggerthanW1,p(Ω).Next,usingrevisereverseHolderinequalityweprovethatifωcisuniformlyp-think,thenthereexistsaneighborhoodUofp,suchthatforallt∈U,theweaksolutionsofequationcorrespondingtareboundeduniformly.Finally,wegetthestabilityofweaksolutionsonexponentp.

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简介：Foraclassofmixedinitial-boundaryvalueproblemforgeneralquasilinearhyperbolicsystems,thispaperestablishesthelocalexactboundarycontrollabilitywithboundarycontrolsonlyactingononeend.Asanapplication,theauthorsshowthelocalexactboundarycontrollabilityforakindofnonlinearvibratingstringproblem.

简介：这篇论文的目的是学习伪的弱解决方案的连续性线性的形式utΔ(u的退化抛物线的方程)=0，

简介：ThispaperconsidersthepointwiseestimateofthesolutionstoCauchyproblemforquasilin-earhyperbolicsystems,whichbasesontheexistenceofthesolutionsbyusingthefundamentalsolutions.Itgivesasharppointwiseestimatesofthesolutionsondomainunderconsideration.Specially,theestimateispreciseneareachcharacteristicdirection.

简介：Theexistenceandnonexistenceofnon-trivialsolutionsfortheCauchyproblemoftheformut=div(|↓Δu|^p-2↓Δu)-u^q,u(x,0)=0,x∈IR^N\{0}arestudied.

简介：Inthispaper,thefirstboundaryvalueproblemforquasilinearequationoftheform△A(u,x)+m∑i=1(e)bi(u,x)/(e)xi+c(u,x)=0,Au(u,x)≥0isstudied.Byusingthecompensatedcompactnesstheory,someresultsontheexistenceofweaksolutionareestablished.Inaddition,undercertainconditiontheuniquenessofsolutionisproved.

简介：Thispaperconcernswithexistenceofgeneralizedsolutionsoffirstboundaryvalueproblemforakindofstronglydegeneratequasilinearparabolicequations.TheauthorassumesthatthecoefficientsintheequationsatisfystronglydegeneratemonotoneconditionandotherweakenedconditionscomparingwiththoseofLadyzenskaja’s.Anexistencetheoremisgivenandproved.

简介：Inthispaper,theauthorstudiestheglobalexistence,singularitiesandlifespanofsmoothsolutionsoftheCauchyproblemforaclassofquasilinearhyperbolicsystemswithhigherorderdissipativetermsandgivestheirapplicationstononlinearwaveequationswithhigherorderdissipativeterms.

简介：Anonlineardifferenceschemeisgivenforsolvingaquasilinearsiagularlyperturbedtwo-pointboundaryvalueproblemwithaturningpoint.Themethodusesnon-equidistantdiscretizationmeshes.ThesolutionoftheschemeisshowntobefirstorderaccurateinthediscreteL^∞norm,uniformlyintheperturbationparameter.

简介：InthispapertheexistenceandmultiplicitiesofpositivesolutionsforaclassofquasilieardifferentialsystemswithsingularnonlinearitiesviaLeray-Schaudetdegreetheoryareestablished.

简介：ＴＨＥＰＡＴＨＷＩＳＥＳＯＬＵＴＩＯＮＦＯＲＡＣＬＡＳＳＯＦＱＵＡＳＩＬＩＮＥＡＲＳＴＯＣＨＡＳＴＩＣＥＱＵＡＴＩＯＮＳＯＦＥＶＯＬＵＴＩＯＮＩＮ　ＢＡＮＡＣＨＳＰＡＣＥⅡＨｕＹａｏｚｈｏｎｇ（ＷｕｈａｎＩｎｓｔ．ｏｆＭａｔｈ．Ｓｃｉ．，Ｃｈｉｎ．Ａ...

简介：Groupclassificationofquasilinearthird-orderevolutionequationsisgivenbyusingtheclassicalinfinitesimalLiemethod,thetechniqueofequivalencetransfor-mations,andthetheoryofclassificationofabstractlow-dimensionalLiealgebras.WeshowthattherearethreeequationsadmittingsimpleLiealgebrasofdimensionthree.Allnon-equivalentequationsadmittingsimpleLiealgebrasarenothingbutthesethree.Furthermore,wealsoshowthatthereexisttwo,five,twenty-nineandtwenty-sixnon-equivalentthird-ordernonlinearevolutionequationsadmittingone-,two-,three-,andfour-dimensionalsolvableLiealgebras,respectively.

简介：我们学习二维的non-self-similar的一个家庭的单个结构quasilinear的全球解决方案和他们的相互作用夸张能量守恒定律。当起始的断绝在仅仅上发生时，为盒子，二拆散统一圆和起始的数据是二个不同经常的状态，全球答案被构造，一些新现象被发现。在分析，我们首先为0t构造答案T，在二个冲击波之间的另一个冲击波发生。最后，我们给答案的大时间行为什么时候t。这种技术不包含维的减小或并列转变。

简介：ThepurposeofthispaperistouseaveryrecentthreecriticalpointstheoremduetoBonannoandMaranotoestablishtheexistenceofatleastthreesolutionsforthequasilinearsecondorderdifferentialequationonacompactinterval[a,b]?R{-u’’=(λf(x,u)+g(u))h(u’),in(a,b),u(a)=u(b)=0underppropriatehypotheses.Weexhibittheexistenceofatleastthree(weak)solutionsand,andtheresultsareillustratedbyexamples.

简介：Inthispaper,weusetheupper-lowersolutionmethodwiththetheoryofmonotoneoperatorstoobtaintheexistenceofcoupledweakquasi-solutionsofthefollowingboundaryvalueproblemforquasilinearellipticsystem