HERMITE ELLIPTIC EQUATIONS

11砒roductlonIt is well－known that the HermitePognomlajs工n＿are肥ry lmmort毗 nd use1SI In m肛nem肌ICa p叮SI0．I上SSSOClltldnllltlNllCtlOO吵。IO)＝二C二二于号三二r口OOCOO口O兀OO tt*OllolllllllDDS——“—————————————————————“—““—““—“一””．\一夕2”!/—————————－”一 一 一———一of L‘冲)nd satisfy the Hermite d伽ential eqllationsJZ。Q一u。·—”““＿2－Iry＿t \．＿ti q＿一1一u＝一Un十11V,讥＝U、1．6,…．I。2—一气—”一J一’一。一…     

临界增长的椭圆型方程广义解的有界性及先验估计

本文证明了椭圆型方程由divA（x，u,u）=B(x,u,u)(在G内)在带权soblev空间中的广义解的有界性，并做出了有界解最大模的先验估计．A（x，u，ζ)和B（x，u，ζ)关于u的增长阶达到了临界指数，而且允许B（x,u,ζ)关于ζ的增长阶γ满足自然增长条件，从而推广和改进了已有的所有结果．     

ON MIN'S ZETA-FUNCTION AND HERMITE ELLIPTIC OPERATOR

In this note,the authors study some fundamental properties on a Min's zeta- function and explore its connection with Hermite elliptic operator.     

NEUMANN PROBLEMS OF A CLASS OF ELLIPTIC EQUATIONS WITH DOUBLY CRITICAL SOBOLEV EXPONENTS

This paper deals with the Neumann problem for a class of semilinear elliptic equations -△u u =|u|2*- 2u μ|u|q- 2u in Ω, u/r=|u|s*- 2u on Ω, where 2* = 2N/N- 2,s*=2(N- 1)/N-2, 1 ＜ q ＜ 2, N ≥ 3, μ＞ 0,γ denotes the unit outward normal to boundaryΩ. By variational method and dual fountain theorem, the existence of infinitely many solutions with negative energy is proved.     

NUMERICAL APPROXIMATIONS OF A SEMI-LINEAR ELLIPTIC PROBLEM

1IntroductionConsidertl1eparameterdependentequationwhereA,ltERarepara1ueterandf:R-RandS:R-RaresinoothoddfunctionwithLetS1:u(x)-u(T-x),r={S1,I}then(l.1)isr-equivariant.Tl1eequality(1.2a)isjustanormalizatiolloffatx=o.Otherwise,onelllayreseektl1eparameterxtoensure(1.2a).To8implifyanalysisweintroduceaSobolevspaceX:=Hl(o,1)anddefilleamappingT:gEL'(o,T)-lL:=TgEXimp1icitly:for(Tg)'V'dx=-jorgl)dx,VvEX,aweakformof(1.1)inXxR2isDuetof(o)=O,theproblem(1.3)(resp.(1))hasatrivialsolutioncurvesC…     

一类高阶椭圆型方程Dirichlet问题

本文讨论了一类奇摄动高阶椭圆型方程Dirichlet问题，利用伸长变量和变界层校正法，得到了问题解的形式渐近展开式．再用微分不等式理论，证明了解的一致有效性．     

INTERFACE PROBLEMS FOR ELLIPTIC DIFFERENTIAL EQUATIONS

ＩＮＴＥＲＦＡＣＥＰＲＯＢＬＥＭＳＦＯＲＥＬＬＩＰＴＩＣＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳＹＩＮＧＬＵＮＧＡＮＡｂｓｔｒａｃｔＡｎｅｗａｐｐｒｏａｃｈｉｓｇｉｖｅｎｔｏａｎａｌｙｓｅｔｈｅｒｅｇｕｌａｒｉｔｙｏｆｓｏｌｕｔｉｏｎｓｎｅａｒｓ...     

THE SINGULARLY PERTURBED BOUNDARY VALUE PROBLEMS FOR HIGHER ORDER SEMILINEAR ELLIPTIC EQUATIONS

Considerasingularlyperturbedproblemforhigherorderselnilinearequationswhereeisasmallpositiveparameter,ndenotesaboundedregioninRe,whereonsignifiesasmoothboundaryofn,misaintegerandjk,gi,k,j=0,'',in--1,aresufficientlysmoothfunctionswithregardtotheirvariablesincorrespondenceranges.Modealwiththesingularperturbationforthesecondorder'ellipticequations[1],[2],thefourthorderequations[3]l[4]andaclassofhigherorderequations[5].Inthispaperttheauthorsconsiderthesingularperturbationforevenmoregeneralhigheror…     

具有两参数的非线性椭圆型方程边值问题解的渐近性态

讨论一类具有双参数的非线性椭圆型方程边值问题. 引入多重尺度变量, 构造问题的形式渐近解. 利用微分不等式理论, 证明边值问题渐近解的存在性和一致有效性. 由解的结构指出, 在两参数一定的情况下,相应问题的解只具有一个边界层.     

NEUMANN PROBLEM OF ELLIPTIC EQUATIONS WITH LIMIT NONLINIEARITY IN BOUNDARY CONDITION

ＮＥＵＭＡＮＮＰＲＯＢＬＥＭＯＦＥＬＬＩＰＴＩＣＥＱＵＡＴＩＯＮＳＷＩＴＨＬＩＭＩＴＮＯＮＬＩＮＩＥＡＲＩＴＹＩＮＢＯＵＮＤＡＲＹＣＯＮＤＩＴＩＯＮ￥ＤＥＮＧＹＩＮＢＩＮＧ；ＷＡＮＧＸＵＪＩＡ；ＷＵＳＨＡＯＰＩＮＧ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅ...     

一类具有非局部边界条件的半线性椭圆型方程奇摄动问题

本文研究了一类具有非局部边界条件的奇摄动半线性椭圆型方程边值问题。在适当的条件下，利用比较定理讨论了问题解的渐近性态。     

THE BOUNDARY VALUE PROBLEMS OF A CLASS OF ELLIPTIC EQUATION WITH A CURVE OF TURNING POINT

The boundary value problems of a class of elliptic equation with a curveof turning point are considered. Using the method of multiple scales and thecomparison theorem, the asymptotic behavior of solution for the boundary valueproblem is studied.     

THE FIRST BOUNDARY VALUE PROBLEM FOR A CLASS OF QUASILINEAR DEGENERATE ELLIPTIC EQUATIONS

In this paper, the first boundary value problem for quasilinear equation of the form △A（u,x）＋∑i=1^m δb^i（u,x）/δxi＋c（u,x）=0,Au（u,x） ≥0is studied. By using the compensated compactness theory, some results on the existence of weak solution are established. In addition, under certain condition the uniqueness of solution is proved.     

一类非线性椭圆方程的解的对称性

本义使用Moving Planes方法证明方程 当x∈R2时, 当x∈R2时的光滑解关于R2中的某一点是对称的.     

关于椭圆型方程解的Liouville定理

在ｂ（ｘ）的较弱条件下，对下面的椭圆型方程，证整解的Ｌｉｏｕｖｉｌｌｅ 定理成立。     

一类二阶退化半线性椭圆型方程边值问题的适定性及解的正则性

本文考虑一类二阶退化半线性椭圆型方程边值问题.由椭圆正则化方法建立能量不等式,利用紧性推理,Banach—Saks定理,弱解与强解一致性,解常微分方程,椭圆型方程正则性定理,迭代方法.极值原理和Fredholm—Riesz-Schauder理论,可得相应线性问题适定性及解的高阶正则性;再由Moser引理和Banach不动点定理可得半线性问题解的存在性.这类问题与几何中无穷小等距形变刚性问题密切相关,其高阶正则性解的存在性对几何应用尤为重要.     

ON INDEFINITE SUBLINEAR ELLIPTIC EQUATIONS

The existence, uniqueness, multiplicity and asymptotic behavior of the solutions to the equation are studied by means of variational and sub-sup-solution methods, where 0 ＜ q ＜ p ＜1, Ω RN with N ＞ 3 is a smooth bounded domain, a, b ∈ L∞(Ω) and λ ∈ R1 is aparameter.     

非自共轭椭圆特征值问题有限元插值校正

本文研究非自共轭椭圆特征值问题有限元插值校正方案.基于插值校正和广义Rayleigh商加速技巧,用三角形线性元二次插值、双二次元双四次插值得到了较好的结果,并用三线性元的三二次捕值将捅值校正推广到三维.     

一类高阶椭圆型方程奇摄动边值问题

本文讨论了一类２ｍ阶奇摄动椭圆型方程边值问题的渐近性态，得到了问题解的一致有效的渐近展开式。     

一类Fuchs型方程的椭圆正则性定理

本文研究了一类锥Sobolev空间上的Fuchs型方程的解的性态,利用Bony的仿微分算子理论的方法,运用仿积、仿复合、仿线性化等工具,并结合Mellin象征的性质,得到了此类方程的椭圆正则性定理.推广了在经典Sobolev空间中的椭圆正则性结果.