共查询到20条相似文献,搜索用时 187 毫秒
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魏公明 《数学年刊A辑(中文版)》2007,(3)
考虑两类带奇性系数发展型p-Laplace不等方程整体非负解的不存在性,也即要证明某些拟线性抛物型方程的非线性Liouville定理.通过先验估计,证明了整体解在某个带参数的函数空间中的不存在性.当只考虑连续整体解时,可选取不带参数的函数空间并证明整体解在其中的不存在性. 相似文献
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考虑两类带奇性系数发展型p-Laplace不等方程整体非负解的不存在性,也即要证明某些拟线性抛物型方程的非线性Liouville定理.通过先验估计,证明了整体解在某个带参数的函数空间中的不存在性.当只考虑连续整体解时,可选取不带参数的函数空间并证明整体解在其中的不存在性. 相似文献
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王向东 《数学物理学报(A辑)》1994,14(1):42-53
该文我们证明了一类齐次线性非一致椭圆型方程广义Green函数的存在性和唯一性,并得到了广义Green函数的一性性质,推广和发展了Gruter,M.和Widman,k.o[2]的相应结果,而且我们证明广义Green函数唯一性的方法与[2]中的方法完全不同. 相似文献
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本文证明了广义Ginzburg-Landau型非线性高阶抛物方程的周期边值问题和Canchy问题广义解和古典解的整体存在性和正则性,并且还证明了解的唯一性和这些解的渐近性质. 相似文献
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该文给出了双调和型抛物方程初值问题解的Schauder估计,并且在适当的空间中证明了解的存在性与惟一性.类似于二阶情形,首先通过Fourier变换得到一个形式解,然后再利用位势理论和逼近方法得到解的正则性、唯一性及存在性.该方法简单而易懂. 相似文献
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本文研究奇异半线性抛物方程ut-Δu+V1(x)u=V2(x)up,x∈Rn\{0},t>0的Cauchy问题解的存在性.这里,V1(x),V2(x)可以在原点具有奇性.利用Kato类函数和Green tight函数及不动点定理证明了问题存在正的奇异解,它在原点具有奇性. 相似文献
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Let G be a finite nonabelian group. Bent functions on G are defined by the Fourier transforms at irreducible representations of G. We introduce a dual basis \({\widehat{G}}\), consisting of functions on G determined by its unitary irreducible representations, that will play a role similar to the dual group of a finite abelian group. Then we define the Fourier transforms as functions on \({\widehat{G}}\), and obtain characterizations of a bent function by its Fourier transforms (as functions on \({\widehat{G}}\)). For a function f from G to another finite group, we define a dual function \({\widetilde{f}}\) on \({\widehat{G}}\), and characterize the nonlinearity of f by its dual function \({\widetilde{f}}\). Some known results are direct consequences. Constructions of bent functions and perfect nonlinear functions are also presented. 相似文献
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Gelfer函数与Yamashita问题邹中柱(湖南怀化师范专科学校,湖南怀化418008)1991年7月19日收到,1992年11月24日收到修改稿.若函数在单位圆盘中解析,且对于一切都有则称函数[2],记其全体为G,并用G表示其单叶子类.显然,当... 相似文献
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Renata Długosz Piotr Liczberski Edyta Trybucka 《Complex Analysis and Operator Theory》2018,12(5):1321-1335
The paper concerns investigations of holomorphic functions of several complex variables with a factorization of their Temljakov transform. Firstly, there were considered some inclusions between the families \(\mathcal {C}_{\mathcal {G}},\mathcal {M}_{\mathcal {G}},\mathcal {N}_{\mathcal {G}},\mathcal {R}_{\mathcal {G}},\mathcal {V}_{\mathcal {G}}\) of such holomorphic functions on complete n-circular domain \(\mathcal {G}\) of \(\mathbb {C}^{n}\) in some papers of Bavrin, Fukui, Higuchi, Michiwaki. A motivation of our investigations is a condensation of the mentioned inclusions by some new families of Bavrin’s type. Hence we consider some families \(\mathcal {K}_{ \mathcal {G}}^{k},k\ge 2,\) of holomorphic functions f : \(\mathcal {G}\rightarrow \mathbb {C},f(0)=1,\) defined also by a factorization of \( \mathcal {L}f\) onto factors from \(\mathcal {C}_{\mathcal {G}}\) and \(\mathcal {M} _{\mathcal {G}}.\) We present some interesting properties and extremal problems on \(\mathcal {K}_{\mathcal {G}}^{k}\). 相似文献
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Luo Xuebo 《偏微分方程(英文版)》1990,3(1)
Using Bargmann's transformation and some basic results of theory of analytic functions with several complex variables, we have disscussed two classes of LPDOs in this paper. We prove that each operator of one class of them is surjective both from G to G and from L² to L², but not injective, and each operator of another class is injective from G to G but not surjective. And in the letter case, the necessary and suffcient conditions for the corresponding equations to be solvable in G are given. 相似文献
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§1 IntroductionIn[1],wehaveintroducedtheconceptoftheGclassoffunctionsintheparabolicclass,andhaveprovedtheHldercontinuityofthiskindoffunctions.Theintroductionoftheconceptcontributestotheproofoftheregularityandexistenceofthesolutionforthefirstboundaryvalueproblemofparabolicequationindivergenceform.Here,weconsidertheapplicationsoftheGclassoffunctionsintheparabolicclasstothefirstboundaryvalueproblemofparabolicequation.Asweknow,ithasreceivedextensivestudyforthefirstboundaryvalueproblemofthefoll… 相似文献
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H. Vernaeve 《Monatshefte für Mathematik》2014,173(3):433-439
We investigate the topological density of various subalgebras of regular generalized functions in the Colombeau algebra $\mathcal{G }(\varOmega )$ of generalized functions with its natural (so-called sharp) topology. 相似文献
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Let G/K be a semisimple orbit of the adjoint representation of a real connected
reductive Lie group G. Let K1 be any closed subgroup of K containing the commutant of
the identity component of K. We prove that the geodesic flow on the symplectic manifold
T*(G/K1), corresponding to a G-invariant pseudo-Riemannian metric on G/K1 which is induced
by a bi-invariant pseudo-Riemannian metric on G, is completely integrable in the class
of real analytic functions, polynomial in momenta. To this end we study the Poisson geometry
of the space of G-invariant functions on T*(G/K) using a one-parameter family of moment
maps. 相似文献