简介:InthispaperwedevelopakindofdissipativediscreteschemeforthecomputationofhomoclinicorbitsnearTB-pointinHamiltoniansystems.Itisprovedbyusingcontinuationmethodthatwhenthedissipativetermanditscoefficientaresuitablychosen,thisschemepossessesdiscretehomoclinicorbits,whichapproximatethecontinuoushomoclinicorbitswithsecondorderaccuracyw.r.totime-stepsize.
简介:让b=(b_1,···,b_m),b_i∈Λ_(β_i)(R~n),1≤i≤m,0<β_i<β,0<β<1,[b,T]f(x)=∫_(R~n)(K是aCalderon-Zygmund的b_1(x)-b_1(y))···(b_m(x)-b_m(y))K(x-y)f(y)dy,核。在这篇论文,我们显示出那[b,T]从L~p(R~n)toF_p~被围住(β,∞)(R~n),以及[b,从L~p(R~n)的I_α]到F_q~(β,∞)(R~n),在哪儿1/q=1/p-α/n。
简介:Inthispaper,weareconcernedwiththesymmetricpositivesolutionsofa2n-orderboundaryvalueproblemsontimescales.Byusinginductionprinciple,thesymmetricformoftheGreen’sfunctionisestablished.Inordertoconstructanecessaryandsufficientconditionfortheexistenceresult,themethodofiterativetechniquewillbeused.Asanapplication,anexampleisgiventoillustrateourmainresult.
简介:Anumbilicalfreeorientedhypersurfacex:M→Rnwithnon-zeroprincipalcurvaturesiscalledaLaguerreisoparametrichypersurfaceifitsLaguerreformC=iCiωi=iρ1(Ei(logρ)(rri)Ei(r))ωivanishesandLaguerreshapeoperatorS=ρ1(S1rid)hasconstanteigenvalues.Hereρ=i(rri)2,r=r1+r2+···+rn1n1isthemeancurvatureradiusandSistheshapeoperatorofx.{Ei}isalocalbasisforLaguerremetricg=ρ2IIIwithdualbasis{ωi}andIIIisthethirdfundamentalformofx.Inthispaper,weclassifyallLaguerreisoparametrichypersurfacesinRn(n>3)withtwodistinctnon-zeroprincipalcurvaturesuptoLaguerretransformations.
简介:在这份报纸,我们学习最少的精力的存在包含部分拉普拉斯算符操作员的一个Kirchhoff类型问题的改变症状的解决方案。由使用限制变化方法和量的变丑词根,我们获得一个最少的精力节的答案u为给定的问题的b。而且,我们证明ub严格地比大两次扎根的州的精力。我们也给u是的bb0,在b被认为是一个积极参数的地方。
简介:本文中,我们研究一类由极大Bochner—Riesz算子和Lipschtz函数A生成的多线性算子,获得了它的(Lp,上q)型,而且我们还将证明此算子从Lebesgue空间到Lipschtz空间、从Herz空间到Campanato空间和从Lp空间到Tribel—Lizorkin空间的有界性.
简介:LetM^nbeaclosedspacelikesubmanifoldisometricallyimmersedindeSitterspaceSp^(n+p)(c),DenotebyR,HandSthenormalizedscalarcurvature,themeancurvatureandthesquareofthelengthofthesecondfundamentalformofM^n,respectively.SupposeRisconstantandR≤c.ThepinchingproblemonSisstudiedandarigiditytheoremforM^nimmersedinSp^(n+p)(c)withparallelnormalizedmeancurvaturevectorfieldisproved.Whenn≥3,thepinchingconstantisthebest.Thus,themistakeofthepaper“Space-likehypersurfacesindeSitterspacewithconstantscalarcurvature”(seeManusMath,1998,95:499-505)iscorrected.Moreover,thereductionofthecodimensionwhenM^nisacompletesubmanifoldinSp^(n+p)(c)withparallelnormalizedmeancurvaturevectorfieldisinvestigated.