ESTIMATES FOR DISCRETE SPECTRUMOF A CERTAIN SYSTEM

1.IntroductionCanyouheartheshapeofadrum?ProfessorProtteraskedinhisrevisitedpaperrll'Usually,thiskindofproblemscanmathematicallybesolvedbyestimatingtheboundsoftheeigenvaluestopolyharmonicoperators.IfonestrikessimultaneouslyNdrumsmadebythesamematerialandpossessingthesamesize,weshouldaskthatcanyouheartheshapeofthedrums?Toanswerthisquestion,onemightconsideraneigenvalueproblemforacertainsystemasfollows:wherefiisaboundedsmoothdomaininRe(m22),u=(al)ro,'',urn)istheoutwardunitnormaltotheboundaryoffi…     

ON SEMILINEAR ELLIPTIC EQUATIONS WITHCONCAVE AND CONVEX NONLINEARITIES IN RN

1IntroductionInthispapertweconsiderthesemilinearellipticproblemwhereA>oisarealparameter,o2.(a2)5(x)ELCc(R"),Otb(x)3OinRNandb(x)EH'(R"),herep'=the.TheSobolevspaceD3l'(RN)isdefinedasthecompletionofCg(R")intheL'(R")normoflvuI.Suchproblemsoccurinvariousbranchesofmathematicalphysicsandpopulationdynamics,andsublinearanaJoguesorsuperline…     

双退化拟线性椭圆型方程Keldys-Fichera障碍问题

讨论一类双退化散度型拟线性椭圆型方程的Keldys-Fichera障碍问题,证明了解的存在性.     

INEQUALITIES FOR EIGENVALUES OF THE POLYHARMONIC OPERATOR Δ~p

In this paper we consider the bounds of the eigenvalues for a class of polyharmonic operators andobtain the bounds for(n 1)th eigenvalue interm of the first n eigenvalues.Those estimates do notdepend on the domain in which the problem is considered.     

一类拟线性方程组的可解性

本文利用上下解方法和Leray—Schauder不动点定理证明了一类拟线性方程组弱解的存在性定理．同时研究了方程组解的唯一性做为定理的应用，给出了一个实例．     

调和算子二次式的离散谱估计

[1]和[2]给出了调和算子的离散谱估计,其后又出现了对重调和算子及任意偶数阶调和算子的离散谱估计.本文将讨论调和算子二次式的离散谱估计,它在物理学及弹性力学领域有着重要的理论意义和应用价值.     

偶数阶调和算子△~(2m)的特征值界的估计

设Ω■R~m,m≥2,是边界充分光滑的有界区域,若正数ι满足下列三条件之一:1.l=2~k;2.l=2_0~(k k_1-1) 2~k_0-1,3.l=2~k_0 k_1-2~k,k=0,1,2,…,k_0,k_1=1,2,…,△~(2l)u-λu=0,x∈Ω,则问题u=аu/аn=…=а~(2l-1)u/аn~(2l-1)=0,x∈аΩ,（n是αΩ的单位外法向）的第n 1个特征值λ_(n 1)有下述隐式和显式表示的界     

THE GENERALIZED SINE-GORDEN EQUATIONS AND THEIR GEOMETRIC ASPECTS

§1 INTRODUCTION The work on"Lie group and KDV equations" has been done in [1]. From the structure equations of certain Lie Group, a class of evolution equations of Sine-Gorden type may be achieved. In this paper from a new viewpoint introduced in [2], we will derivea class     

BOUNDARY VALUE PROBLEM FOR DEGENERATE AND SINGULAR p-LAPLACIAN SYSTEMS

In this article, using the contraction mapping principle and the shooting method, the authors obtain the existence and uniqueness of the local solution and the global solution to a class of quasilinear elliptic systems with p-Laplacian as its principal.They also obtain the continuous dependence of the solutions on the boundary data.     

类p-Laplacian方程的特征值问题

本文考虑类p-Laplacian方程-div(a(|Du|~p)|Du|~(p-2)Du)=λf(x,u),x∈Ω,u=0,x∈Ω的特征值问题,其中ΩR~n(n≥2)是有界光滑区域.当λ>0充分小,本质上仅在凸函数的假设下,得到了性质完全不同的两个特征函数的存在性,作为定理的应用,文中给出了两个实例.