简介:利用变分原理研究超线性常微分p-Laplace系统周期解的存在性.在带有脉冲和阻尼作用项时,根据易一型山路定理,得到了系统多重周期解的存在性.
简介:利用非线性增生映射值域的扰动定理,研究了非线性椭圆边值问题(1)在Ls(Ω)空间中解的存在性,其中max(N,2)≤p≤s<+∞.(1){-div{(C(x)+|▽u|2)p-2/2▽u}+|u|p-2u+g(x,u(x))=fa.e.x∈Ω-〈n,(C(x)+|▽u|2)p-2/2▽u〉∈βx(u(x))a.e.x∈Γ这里f∈Ls(Ω)给定,Ω()RN为有界锥形区域,n为Γ的外法向导数,g:Ω×R→R满足Caratheodory条件且对()x∈Γ,βx是正常、凸、下半连续函数ψx=ψ(x,·)的次微分,其中ψ:Γ×R→R.本文是对笔者以往一些工作的继续和补充.
简介:利用临界点理论研究具有部分周期位势的非自治常p-Laplace系统周期解的存在性.在具有p-线性增长非线性项时,根据广义鞍点定理,得到了系统多重周期解存在的充分条件.
简介:研究了一类具有Robin边值条件的p-Laplace方程解的存在性.利用Sobolev紧嵌入定理以及给定的假设条件证明了该类方程的能量泛函具有山路型结构并且满足(PS)条件,从而根据山路引理得到了该类方程在Sobolev空间W1,p(Ω)中非平凡弱解的存在性.
简介:Inthispaper,thetheoremsconcerningthesummationofFourierserieswithparameteraregivenbyusingtheLaplacetransforms.BymeansoftheknownresultofLaplacetransforms,manynew,importantproblemsofsummationofFourierserieswithparameterinmechanicscanbesolved.
简介:AnewmethodforapproximatingtheinerseLaplacetransformispresented.WefirstchangeourLaplacetransformequationintoaconvolutiontypeintegralequation,whereTikhonovregularizationtechniquesandtheFouriertransformationareeasilyapplied.WefinallyobtainaregularizedapproximationtotheinverseLaplacetransformasfinitesum
简介:Inthepresentpaper,wehaveconsideredtheapproximationofanalyticfunctionsrepresentedbyLaplace-Stieltjestransformationsusingsequenceofdefiniteintegrals.WehavecharacterizedtheirorderandtypeintermsoftherateofdecreaseofEn(F,b)whereEn(F,b)istheerrorinapproximatingofthefunctionF(s)bydefiniteintegralpolynomialsinthehalfplaneRes≤b〈a.
简介:§0.IntroductionLetXbearealseparableBanachspaceandX*beitsdualspace,LetB(X)betheBorelfield,i.e.,thetopologicalσ-field.Afunctionalu:X→R’iscalledaboundedsmoothfunctional,ifn∈N,f1,…,fn∈X*andφ∈Cb∞(Rn),suchthat
简介:Letfibeaboundedsmoothdomain.Inthispaper,theauthorsdefinetheBesovspacesBpa,pon,establishtheatomicdecompositionofthesespaces,andobtaintheregularityestimateoftheDirichletproblemandtheNeumannproblemfortheLaplaceoperatoronthesespaces.
简介:Inthispaper,weconsidertheCauchyproblemfortheLaplaceequation,whichisseverelyill-posedinthesensethatthesolutiondoesnotdependcontinuouslyonthedata.AmodifiedTikhonovregularizationmethodisproposedtosolvethisproblem.Anerrorestimatefortheaprioriparameterchoicebetweentheexactsolutionanditsregularizedapproximationisobtained.Moreover,anaposterioriparameterchoiceruleisproposedandastableerrorestimateisalsoobtained.Numericalexamplesillustratethevalidityandeffectivenessofthismethod.
简介:Thispaperdevelopsanumericalmethodtoinvertmulti-dimensionalLaplacetransforms.Byavariabletransform,Laplacetransformsareconvertedtomulti-dimensionalHansdorffmomentproblemssothatthenumericalsolutioncanbeachieved.Stabilityestimationisalsoobtained.Numericalsimulationsshowtheefficiencyandpracticalityofthemethod.