简介：Inthispaper,twoexistencetheoremsaregivenconcerningthefollowing3-pointboundaryvalueproblemofsecondorderdifferentialsystemswithimpulses

简介：1.IntroductionInthispaperweconsidertheCauchyproblemforthefastdiffusionequationwheremaxandpositivefunction.Thistypeofequationhasbeenextensivelystudiedasamathematicalmodelofalotofphysicalproblems(see[1-3]).Amajortopicofstudyistheexistenceandnonexistenc...

简介：Inthispaper,byusingthecriticalpointtheory,theexistenceofperiodicandsubharmonicsolutionstoaclassofsecondorderfunctionaldifferenceequationsisobtained.ThemainapproachusedinourpaperisvariationaltechniqueandtheSaddlePointTheorem.Theproblemistosolvetheexistenceofperiodicandsubharmonicsolutionsofsecondorderforwardandbackwarddifferenceequations.

简介：Incontrollednuclearfusiondevicesliketokamaks,plasmaparticlesareconfinedbyclosedmagneticfluxsurfaces.Outsidethelastclosedfluxsurface(LCFS),plasmaisindirectcontactwithasolidwallinthescrape-offlayer(SOL).Duetothedifferent

简介：Inthispaper,westudyanddiscusstheexistenceofmultiplesolutionsofaclassofnon-linearellipticequationswithNeumannboundarycondition,andobtainatleastsevennon-trivialsolutionsinwhichtwoarepositive,twoarenegativeandthreearesign-changing.Thestudyofproblem(1.1):{-△u+αu=f(u),x∈Ω,x∈Ω,δu/δr=0,x∈δΩ,isbasedonthevariationalmethodsandcriticalpointtheory.Weformourconclusionbyusingthesub-supsolutionmethod,MountainPassTheoreminorderintervals,Leray-Schauderdegreetheoryandtheinvarianceofdecreasingflow.

简介：WestudytheexistenceanduniquenessproblemforthenonhomogeneouspressurelessEulersystemwiththeinitialdensitybeingaRadonmeasure.Ouruniquenessresultisobtainedinthesamespaceastheexistencetheorem.Besides,bycounterexampleweprovethatHuang-Wang'senergyconditionisalsonecessaryforournonhomogeneoussystem.

简介：AnexampleofcompletsRiemannianmetricofpositive(ornonnagative)curvatureonR^nsuchasds^2=a(x)dx^2isobtainedbydirectcaculations.Furthermore,byusingageodesicconvexconditionandatheoremforcompletenoncompactRiemannianmanifold,anexistenceresultofperiodicsulutionofprescribedenergyforasingularHamiltoniansystemisalsoobtained.

简介：§1.IntroductionWeconsiderthesingularnonlinearboundaryvalueproblemwherel=v+3/v-1,l+1isthecriticalexponentoftheembeddingofweightedSobolevspaceWt21,2（O,+∞）intoLt2q（O,∞）,v>2.Whenv=N-1wecangettheradialsolutionsofproblemwhere2*=2N/N-2isthecriticalexponentoftheSobolevembeddingH1（Rn）→LQ（RN）.Kurtzhasdiscussedtheexistenceofκ-nodesolutionof（1.1）,（1.2）foreachκ∈NU{0}whenthegrowthrateof|u|l-1u+f（u）islowerthen|u|v+3/v-1i.e.

简介：<正>Inthispaper,anexistenceresultofentropysolutionstosomeparabolicproblemsisestablished.ThedatabelongstoL~1andnogrowthassumptionismadeonthelower-ordertermindivergenceform.

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简介：这篇论文为有Hamiltonian形式的联合BBM方程涉及独居的波浪的轨道的稳定性/不稳定性。明确的独居的波浪答案将首先被得出。然后由详细说明光谱分析和起始的价值问题的解决方案的腐烂的估计，我们获得独居的波浪的轨道的稳定性/instability。

简介：Inthispaperweconsiderthep-Laplaceproblem-εp?pu+V(x)up-1=uq-1,u>0inRNwhere2≤p0andp0issmall.

简介：这份报纸处理坡度关于一个可变度量标准在被拿的一个抽象周期的坡度系统。我们经由一条全球反的定理的申请获得存在和唯一结果。

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简介：Thispaperisasequeltoapreviouspaper(Yang,Y.andZhang,J.H.Existenceofsolutionsforsomefourth-orderboundaryvalueproblemswithparameters.NonlinearAnal.69(2),1364–1375(2008))inwhichthenontrivialsolutionstothefourthorderboundaryvalueproblemswerestudied.Inthecurrentworkwiththesameconditionsnearinfinitybutdifferentnearzero,thepositive,negative,andsign-changingsolutionsareobtainedbythecriticalpointtheory,retractingproperty,andinvariantsets.

简介：Inthispaper,weconsiderexistenceanduniquenessofpositivesolutionstothreecouplednonlinearSchrdingerequationswhichappearinnonlinearoptics.Weusethebehaviorsofminimizingsequencesforaboundtoobtaintheexistenceofpositivesolutionsforthreecoupledsystem.Toprovetheuniquenessofpositivesolutions,weusetheradialsymmetryofpositivesolutionstotransformthesystemintoanordinarydifferentialsystem,andthenintegratethesystem.Inparticular,forN=1,weprovetheuniquenessofpositivesolutionswhen0≤β=μ1=μ2=μ3orβ>max{μ1,μ2,μ3}.

简介：在我们证明内部坡度和秒的这篇论文，衍生物为Ricci或Schouten张肌的特征值的对称的功能决定的充分非线性的椭圆形的方程的一个班估计。当时，作为应用，我们证明方程的答案的存在歧管局部地正式扁平的反对或Ricci弯曲是积极的。

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简介：在这份报纸，我们证明为非线性的进化方程ut=螖u+螞u的起始边界的价值问题吗？u3为所有k鈮?在Sobolev空间Hk拥有一个全球引起注意的人0，它吸引Hk的任何围住的域(在Hk标准的惟)。这结果被为操作员的线性semigroup使用一种重复技术和整齐估计建立，它从盒子k扩大古典结果[0，1]到盒子k[0，鈭?。

简介：我们学习形式的非线性的堕落椭圆形的问题的解决方案的存在结果，—div(一(x，u，∇u))在Ω的=F，在Ω是ℝN,N≥的一个围住的领域的地方2，一：Ω×ℝ×ℝN→ℝN是Carathéodory功能令人满意自然生长条件和coercivity调节，但是他们验证仅仅大单音的强健。第二条款F属于W−1,p′(Ω,w*)。存在结果被使用L1-version证明薄荷的词根。