一类退缩的椭圆型方程弱解的正则性

本文给出了一类退缩的拟线性椭圆型方程－Ｄｉｖ「↓ｕ｜＾ｐ－２↓ｕ＋Ｆ（ｘ,ｕ）」＝Ｂ（ｘ,ｕ,↓ｕ）在Ｗ＾１,ｐ（Ω）中弱解的Ｃ＾１,λｌｏｃ（Ω）正则性,其中Ω为Ｒ＾Ｎ中行一区域。     

微分方程-u"=λ~2u |u''''|~β边值问题正解的存在唯一性

本文讨论一类不满足 Ｎａｇｕｍｏ条件的微分方程边值问题－ｕ＂＝λ２＋｜ｕ＇｜β，ｕ（０）＝ｕ（１）＝０正解的存在唯一性问题，其中β＞２为常数，λ＞０为参数．证明了对每一β＞２，存在λ＝λ（β）∈（０，π），边值问题存在属于Ｃ１［０，１］正解当且仅当λ∈（λ，π），此时正解唯一，当λ＝λ（β）时，边值问题存在正解。 ｕ∈Ｃ１（０，１）∩Ｃ［０，１］，ｕ＇（０）＝∞，ｕ＇（１）＝－∞，并证明ｌｉｍ　λ（β）＝π     

共振情形下次线性椭圆偏微分方程的解

研究了共振下的微分方程Δｕ＋λ_１ｕ＋ｇ（ｘ，ｕ）＝０，ｘ∈?Ω；ｕ｜_?Ω＝０．在ｇ（ｘ，ｕ）关于ｕ次线性的情形，证明了解的存在性，从而部分地回答了Ｆｉｇｕｅｉｒｅｄｏ ａｎｄ Ｍａｓｓａｂｉ的一个问题．     

一类非线性积分方程正解的存在唯一性

本文研究积分方程ｕ（ｘ）＝λ∫_Ωｋ（ｘ，ｙ）ｆ（ｙ，ｕ（ｙ））ｄｙ，λ＞０及其它的非线性摄动ｕ（ｘ）＝λ∫_Ωｋ（ｘ，ｙ）ｆ（ｙ，ｕ（ｙ））ｄｙ＋Ｇ（ｕ（ｘ）），在ｋ（ｘ，ｙ）非负可测，ｆ（ｘ，ｕ），Ｇ（ｕ）满足一定条件下，得到所述方程解的存在唯一性及其迭代逼近．     

非线性抛物型方程的爆破

本文考虑非线性抛物型方程ｕｔ＝ｅ＾ｕ（△ｕ＋ｕ），ｘ∈Ω，证明在Ω上当－△ｕ＝λｕ的第一特征值λ１（Ω）〈１时，解ｕ有有限时刻爆破。     

非线性抛物型方程解的爆破

本文考虑非线性抛物型方程ｕｔ＝ｅｕ（Δｕ＋ｕ），ｘ∈Ω，证明在Ω上当－Δｕ＝λｕ的第一特征值λ１（Ω）＜１时，解ｕ在有限时刻爆破．     

二维Landau-Lifshitz静态方程组的渐近性质

在本文中，我们讨论了ｕ∧（－Δｕ＋λ（ｕ，ｎ）ｎ）＝０，｜ｕ｜＝１，ｘ∈Ｂ１和ｕ＝（ｘ１，ｘ２，０）ｘ∈Ｂ１的轴对称解ｕλ的渐近行为，其中Ｂ１是Ｒ２中单位圆，ｕ＝（ｕ１，ｕ２，ｕ３）．我们证明了ｕλｕ∞在Ｈ２Ｂ１＼Ｂε，Ｒ３中．     

二阶微分方程Neumann边值问题正解存在性

本文利用锥不动点定理证明了－ｕ"＋Ｍｕ＝ｆ（ｔ,ｕ）,ｕ′（０）＝ｕ′（１）＝０和ｕ"＋Ｍｕ＝ ｆ（ｔ,ｕ）,ｕ′（０）＝ｕ′（１）＝ ０两个二阶微分方程 Ｎｅｕｍａｎｎ边值问题正解的存在性。     

｛0,1,3｝问题摄动形式所对应的测度

给定实数λ,α以及Ｒ上（以λ,α为参数）的压缩自相似映射Ｓ１（ｘ）＝λｘ, Ｓ２（ｘ）＝ λｘ＋ａ, Ｓ３（ｘ）＝ λｘ＋３,记满足测度方程ｖ＝（１／３）∑ｉ＝１ｖｏＳｉ－１的唯一概率测度为ｕλ,α本文得到：（１）当固定 λ∈Ａ Ｅ（１／３, ２／５）时,则在 Ｌｅｂｅｓｇｕｅ测度意义下,对于 ａ．ｅ．的 ａ∈（０,１）,测度 ｕλ,α绝对连续,且存在平方可积密度．（２）若λ－１是 Ｐ．Ｖ．数,且 α是λ的有理系数多项式,则测度ｕλ,α是奇异测度．     

二阶Hamilton系统-L(t)u+W′_u(t,u)=0同宿轨道的存在性

本文利用临界点理论中的山路引理，证明了二阶Ｈａｍｉｌｔｏｎ系统 －Ｌ（ｔ）ｕ＋ Ｗ′ｕ（ｔ，ｕ）＝０存在非平凡的同宿轨道，其中Ｌ（ｔ）ｙ·ｙ≥λ｜ｙ｜２，ｙ∈Ｒｎ，λ＞０，Ｌ（ｔ）和 Ｗ（ｔ，ｕ）关于变量ｔ没有周期性假设．     

On a class of self-similar processes with stationary increments in higher order Wiener chaoses

We study a class of self-similar processes with stationary increments belonging to higher order Wiener chaoses which are similar to Hermite processes. We obtain an almost sure wavelet-like expansion of these processes. This allows us to compute the pointwise and local Hölder regularity of sample paths and to analyse their behaviour at infinity. We also provide some results on the Hausdorff dimension of the range and graphs of multidimensional anisotropic self-similar processes with stationary increments defined by multiple Wiener–Itô integrals.     

A REPRESENTATION FORMULA RELATED TO SCHR(O)DINGER OPERATORS

Schr(o)dinger operator is a central subject in the mathematical study of quantum mechanics.Consider the Schrodinger operator H = -△ V on R, where △ = d2/dx2 and the potential function V is real valued. In Fourier analysis, it is well-known that a square integrable function admits an expansion with exponentials as eigenfunctions of -△. A natural conjecture is that an L2 function admits a similar expansion in terms of "eigenfunctions" of H, a perturbation of the Laplacian (see [7], Ch. Ⅺ and the notes), under certain condition on V.     

On a class of Riemann surfaces

It is considered the class of Riemann surfaces with dimT1 = 0, where T1 is a subclass of exact harmonic forms which is one of the factors in the orthogonal decomposition of the spaceΩH of harmonic forms of the surface, namely The surfaces in the class OHD and the class of planar surfaces satisfy dimT1 = 0. A.Pfluger posed the question whether there might exist other surfaces outside those two classes. Here it is shown that in the case of finite genus g, we should look for a surface S with dimT1 = 0 among the surfaces of the form Sg\K , where Sg is a closed surface of genus g and K a compact set of positive harmonic measure with perfect components and very irregular boundary.     

CONTENTS OF VOLUME 30

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Instructions for contributions

正Applied Mathematics-A Journal of Chinese Universities,Series B(Appl.Math.J.Chinese Univ.,Ser.B)is a comprehensive applied mathematics journal jointly sponsored by Zhejiang University,China Society for Industrial and Applied Mathematics,and Springer-Verlag.It is a quarterly journal with     

Journal of Mathematical Research with Applications Guide for Authors

正Journal overview:Journal of Mathematical Research with Applications(JMRA),formerly Journal of Mathematical Research and Exposition(JMRE)created in 1981,one of the transactions of China Society for Industrial and Applied Mathematics,is a home for original research papers of the highest quality in all areas of mathematics with applications.The target audience comprises:pure and applied mathematicians,graduate students in broad fields of sciences and technology,scientists and engineers interested in mathematics.     

Staircase transportation problems with superadditive rewards and cumulative capacities

A cumulative-capacitated transportation problem is studied. The supply nodes and demand nodes are each chains. Shipments from a supply node to a demand node are possible only if the pair lies in a sublattice, or equivalently, in a staircase disjoint union of rectangles, of the product of the two chains. There are (lattice) superadditive upper bounds on the cumulative flows in all leading subrectangles of each rectangle. It is shown that there is a greatest cumulative flow formed by the natural generalization of the South-West Corner Rule that respects cumulative-flow capacities; it has maximum reward when the rewards are (lattice) superadditive; it is integer if the supplies, demands and capacities are integer; and it can be calculated myopically in linear time. The result is specialized to earlier work of Hoeffding (1940), Fréchet (1951), Lorentz (1953), Hoffman (1963) and Barnes and Hoffman (1985). Applications are given to extreme constrained bivariate distributions, optimal distribution with limited one-way product substitution and, generalizing results of Derman and Klein (1958), optimal sales with age-dependent rewards and capacities.To our friend, Philip Wolfe, with admiration and affection, on the occasion of his 65th birthday.Research was supported respectively by the IBM T.J. Watson and IBM Almaden Research Centers and is a minor revision of the IBM Research Report [6].