类退化椭圆型方程的边值问题

在由光滑Jordan曲线Ω:H(x,y)=0围成的区域Ω中,考虑方程(u)≡A_0H~au_(xx)+2B_0H~βu_(xy)+C_0H~yu_(yy)+au_x+bu_y+cu=0, (1) 对0<λ<1,我们规定以C~(m+λ)(Ω)表示C~m(Ω)中其m阶导数在Ω上满足具有指数λ的Holder条件的那些函数所成的类。我们假设:方程(1)的系数A_0、B_0、C_0、a、b、c∈CC~λ(Ω),H∈C~(2+λ)(Ω),并且c0,常数a、β、r>0。不妨设在Ω中H(x,y)>0,而在Ω上A_0、B_0、C_0均不恒为零。 假设在Ω中B_0~2H~(2β)-A_0C_0H~(a+γ)<0,即方程是椭圆型的。由假设可知2βα+γ。显然,方程(1)在整个边界Ω上呈退化。而以往的许多工作,如丁正中和他的文献中指出的     

The Singularly Perturbed Boundary Value Problems for Semilinear Elliptic Equation

The singularly perturbed boundary value problems for the semilinear elliptic equation are considered. Under suitable conditions and by using the fixed point theorem, the existence, uniqueness and asymptotic behavior of solution for the boundary value problems are studied.     

The Singularly Perturbed Boundary Value Problems for Semilinear Elliptic Equation

The singularly perturbed boundary value problems for the semilinear elliptic equation are considered. Under suitable conditions and by using the fixed point theorem, the existence, uniqueness and asymptotic behavior of solution for the boundary value problems are studied.     

拟线性椭圆型方程奇摄动边值问题

本文讨论了拟线性椭圆型方程奇摄动Robin边值问题。在适当的条件下，利用不动点定理，研究了边值问题解的存在唯一性及其渐近性态。     

Poisson Kernel for a Degenerate Elliptic Equation and Application to Boundary Value Problems

In this paper we consider the Dirichlet problem to a degenerate elliptic equation in a domain whose interior contains a degenerate surface. By means of the method of expansion of Poisson kernel and applying the properties of special functions, we obtain the twice continuously differentiable solution of the problem on the entire space including infinity.     

具有转向点的椭圆型方程奇摄动边值问题

本文讨论了具有转向点的奇摄动椭动椭圆型方程边值问题,利用多重尺度法和比较定理,确定了边值问题解的渐近性态。     

退化椭圆型方程的一个边值问题

本文主要讨论在ｘ 轴上退化的二阶椭圆型偏微分方程的混合边值问题．     

一类半线性椭圆型方程奇摄动广义边值问题

讨论了一类非线性椭圆方程奇摄动广义边值问题。在适当的条件下,研究了边值问题广义解的存在、唯一性及其渐近性态。     

一类四阶半线性椭圆型方程非局部边值问题(英文)

本文研究了一类四阶半线性椭圆型方程奇摄动非局部问题.     

Initial Value Problems of the Sine-Gordon Equation and Geometric Solutions

Recent results using inverse scattering techniques interpret every solution φ(x, y) of the sine-Gordon equation as a nonlinear superposition of solutions along the axes x=0 and y=0. This has a well-known geometric interpretation, namely that every weakly regular surface of Gauss curvature K=−1, in arc length asymptotic line parametrization, is uniquely determined by the values φ(x, 0) and φ(0, y) of its coordinate angle along the axes. We introduce a generalized Weierstrass representation of pseudospherical surfaces that depends only on these values, and we explicitely construct the associated family of pseudospherical immersions corresponding to it.Mathematics Subject Classifications (2000): 53A10, 58E20.     

一类拟线性椭圆方程边值问题弱解的研究

本文应用上、下解方法和 Leray-Schauder不动点定理 ,证明了一类拟线性椭圆方程边值问题弱解的存在性 ,并且给出了一个应用实例     

Mixed Boundary Value Problems for the Helmholtz Equation in a Quadrant

The main objective is the study of a class of boundary value problems in weak formulation where two boundary conditions are given on the half-lines bordering the first quadrant that contain impedance data and oblique derivatives. The associated operators are reduced by matricial coupling relations to certain boundary pseudodifferential operators which can be analyzed in detail. Results are: Fredholm criteria, explicit construction of generalized inverses in Bessel potential spaces, eventually after normalization, and regularity results. Particular interest is devoted to the impedance problem and to the oblique derivative problem, as well.     

KdV-KSV方程的初边值问题

本文证明了KdV－KSV方程的周期边值问题和Cauchy问题广义解和古典解的整体存在性、正则性及唯一性．     

一类高阶拟线性椭圆型方程奇摄动边值问题

本文讨论了一类拟线性椭圆型方程奇摄动Dirichlet边值问题．在适当的条件下，利用不动点定理，研究了边值问题解的存在唯一性及其渐近性态．     

Sine-Gordon方程的动态边界反馈镇定

考虑一端固定,控制输入在另一端的Sine-Gordon方程的动态边界反馈镇定问题.我们给出闭环系统的适定性,并利用乘子方法得到在动态边界反馈控制下闭环系统的多项式衰减率.     

Maximum Principles for a Class of Nonlinear Elliptic Boundary Value Problems

The Hopf＇s maximum principles are utilized to obtain maximum principles for functions defined on solutions of nonlinear elliptic equations in divergence form （g（u）u,i）,i ＋f（x,u,q）=0（q=｜△↓u｜^2）, subject The principles derived may be used to deduce bounds on the gradient q.     

紧黎曼流形上的椭圆边界值问题

讨论一类非齐次非线性椭圆边界值问题.利用极大值原理证明了该问题解的梯度估计.作为它的应用得到了解的效率比估计.