简介：Theexistenceofinfinitelymanysolutionsfortheequation

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：Mathematicalprogramswithcomplementarityconstraints(MPCC)isanimportantsubclassofMPEC.ItisanaturalwaytosolveMPCCbyconstructingasuitableapproximationoftheprimalproblem.Inthispaper,weproposeanewsmoothingmethodforMPCCbyusingtheaggregationtechnique.AnewSQPalgorithmforsolvingtheMPCCproblemispresented.Ateachiteration,themasterdirectioniscomputedbysolvingaquadraticprogram,andthereviseddirectionforavoidingtheMaratoseffectisgeneratedbyanexplicitformula.Asthenon-degeneracyconditionholdsandthesmoothingparametertendstozero,theproposedSQPalgorithmconvergesgloballytoanS-stationarypointoftheMPECproblem,itsconvergencerateissuperlinear.Somepreliminarynumericalresultsarereported.

简介：1.IntroductionTherearealotofresultsaboutHammersteinintegralequations(see[1]),butsupen-linearproblemsaredifficult;thereareonlyafewresultsaboutit.In[2,3]theauthorsstudysuperliniearintegralequations;in[4]theauthorsstudysystemofsuperlinearintegralequatio...

简介：在这份报纸，在证明二存在的作者目的形式$$\left的部分微分边界价值问题结果({{P_{一，b}}}\right)\left\{{_{u\left(0\right)=u\left(1\right)=0，{D^{\alpha-3}}u\left(0\right)=一，u'\left(1\right)=-b}^{{D^\alpha}u\left(x\right)+f\left({x，u\left(x\right)}\right)=0，x\in\left({0,1}\right)}}\right.$$3<4，D是标准Riemann-Liouville部分衍生物并且一，b是nonnegative常数。首先，作者建议那f(x，t)=p(x)t,与(1，1)并且是的pnonnegative可能在x=单个的连续功能0或x=1并且满足与Karamata常规变化理论有关的一些条件。一些潜在的功能和Sch上的联合锋利的估计?uder修理了点定理，作者证明问题的一个唯一的积极连续答案的存在(P0,0)。如此的一个答案上的全球估计也被获得。为了说第二存在，结果，作者假定那一，b是nonnegative常数以便+b>0并且f(x，t)=t(x，t)，与(x，t)nonnegative是连续的工作在(0，吗1)牵慦散猠摥浩湥獴映潲?慈桩?楒敶?慂楳?敷敲椠癮獥楴慧整??洠瑥潨?慢敳?湯攠晦'太B爠湡敧?剅?慷?獵摥琠?獡敳獳攠潣祳瑳浥爠獩?景倠??琨敨琠瑯污漠??倠??敳獮瑩癩汥?湡?捡畣慲顰?顰？？

简介：Inthispaper,theauthordiscussesthemultiplepositivesolutionsforaninfiniteboundaryvalueproblemoffirstorderimpulsivesuperlinearintegro-differentialequationsonthehalflinebymeansofthefixedpointtheoremofconeexpansionandcompressionwithnormtype.