带可变参数四阶奇异边值问题正解的存在性

本文研究了带有一个可变参数的四阶奇异边值问题,利用Banach空间的不动点理论,在非常弱的条件下,获得了带可变参数四阶奇异边值问题存在正解的结果.     

半导体物理中的一个两点边值问题

本文研究了在半导体流的区域提纯过程中提出的两点边值问题解的存在性，我们用上、下解方法和Ｓｓｈａｕｄｅｒ不动点定理证明了如果Ｑ＝２Ａ３Ｒｅ，其中Ａ是表面速率，Ｒｅ是Ｒｅｙｎｏｌｄｓ数，则当０ Ｑ １２．６８时，该问题有解． 对［１］的结果（０ Ｑ＜８．５１时，此问题的解存在）进行了重要的改进．     

半导体物理中的一个两点边值问题

本文研究了半导体流的表面张力进行区域提纯问题中提出的两点边值问题解的存在性 ,我们用上、下解方法和 Schauder不动点定理证明了如果 Q=2 A3 Re,其中 A是表面速率 ,Re是 Reynolds数 ,则当 0 Q 1 3.2 1时 ,该问题有解 ,对最近的结果 ( 0 Q 1 2 .6 8时 ,此问题的解存在 )进行了重要的改进     

关于稳态反应扩散对流方程的死核问题

本文研究带参数λ的稳态反应扩散对流方程△u=λf(u,Du)的死核问题,证明了当函数f满足一定的条件时,对每个有界光滑区域Ω存在相应的正数λ(Ω)使当λ>λ(Ω)时该方程在边值条件u=1下的非负解有死核,并讨论了死核随λ的变化情况。     

一类四阶差分方程多点边值问题的正解

为解决多点支撑弹性梁的正解的存在性问题,运用锥上不动点指数理论,研究一类含参四阶差分方程多点边值问题.获得了当参数在一定范围内取值时正解的存在性结果,得到了正解存在的充分条件.     

Solving a nonlinear inverse Robin problem through a linear Cauchy problem

ABSTRACT

Considered in this paper is an inverse Robin problem governed by a steady-state diffusion equation. By the Robin inverse problem, one wants to recover the unknown Robin coefficient on an inaccessible boundary from Cauchy data measured on the accessible boundary. In this paper, instead of reconstructing the Robin coefficient directly, we compute first the Cauchy data on the inaccessible boundary which is a linear inverse problem, and then compute the Robin coefficient through Newton's law. For the Cauchy problem, a parameter-dependent coupled complex boundary method (CCBM) is applied. The CCBM has its own merits, and this is particularly true when it is applied to the Cauchy problem. With the introduction of a positive parameter, we can prove the regularized solution is uniformly bounded with respect to the regularization parameter which is a very good property because the solution can now be reconstructed for a rather small value of the regularization parameter. For the problem of computing the Robin coefficient from the recovered Cauchy data, a least square output Tikhonov regularization method is applied to Newton's law to obtain a stable approximate Robin coefficient. Numerical results are given to show the feasibility and effectiveness of the proposed method.     

On Perturbed Discrete Boundary Value Problems

In this paper, we study nonlinear discrete boundary value problems of the form x ( t +1)= A ( t ) x ( t )+ h ( t )+ k f ( t , x ( t ), k ) subject to Bx (0)+ Dx ( J )= u + k g ( x (0), x ( J ), k ) where k is a "small" parameter. Our main concern is the case of resonance, that is, the situation where the associated linear homogeneous boundary value problem x ( t +1)= A ( t ) x ( t ), Bx (0)+ Dx ( J )=0 admits nontrivial solutions. We establish conditions for the solvability of the nonlinear boundary value problem when k is "small". We also establish qualitative properties of these solutions.     

具有非局部边界的奇异摄动问题的数值解

研究了具有非局部边界的奇异摄动问题。对于正的小摄动参数，其解显示出边界层特性。为了求解该问题，构造了非等距网格上的指数型有限差分。还给出了小参数时的一致收敛性分析，同时给出了一个数值例子。     

Homogenization of Stratified Dilatant Fluid

In this paper we study the behavior of the stationary magnetic hydrodynamical boundary layer of a dilatant fluid flowing through a porous obstacle. We consider a family of boundary value problems with a small parameter where micro-inhomogeneities are concentrated on the boundary of the domain (the original velocity profile depends on a small parameter). We construct an averaged problem and prove convergence of the solution of the original problem to that of the averaged one. Thus we describe the effective behavior of the micro-inhomogeneous fluid.     

关于大几何参数的开顶扁球壳屈曲问题的奇摄动

本文利用修正多重尺度法研究了大几何参数的具有刚性中心的边缘铰接的开顶扁球壳，在复合载荷作用下的非线性稳定问题，求得了扁壳几何参数ｋ值圈套时，本问题的一致有效的渐近解。     

(n,k)-排列图的条件连通度(英文)

点连通度是衡量互联网络容错性的一个重要参数.尽管点连通度能正确地反映了系统的容错性能,但是不能正确反映大规模网络的健壮性能.条件连通度通过对各分支附加一些要求(当整个网络被破坏时)来克服这个缺点.给定一个基于图G的网络和一个正整数l,G的R~l-连通度,记为k~l(G),定义为图G的最小节点子集的节点数,使其去掉后,G是不连通的,且每个分支的最小度至少是l.在本文中,我们得到了(n,k)-排列图的条件连通度k~l(A(_n,k))=[(l+1)k-l](n-k)-l,其中k≥l+2,n≥k+l.     

Existence and multiplicity of solutions for an impulsive boundary value problem with a parameter via critical point theory

In this paper, an impulsive boundary value problem with a parameter is considered. By using critical point theory, some criteria are obtained to guarantee that the impulsive problem has at least one solution, two solutions and infinitely many solutions when the parameter lies in different intervals. The results obtained are also valid and new for a problem discussed in the literature.     

Perturbations for linear difference equations

In this paper we study boundary value problems for perturbed second-order linear difference equations with a small parameter. The reduced problem obtained when the parameter is equal to zero is a first-order linear difference equation. The solution is represented as a convergent series in the small parameter, whose coefficients are given by means of solutions of the reduced problem.     

k次R-对称矩阵的特征值反问题及最佳逼近问题

<正>1引言在[7]中,Trench推广了中心对称矩阵和自反矩阵的概念定义了R-对称矩阵,采用一个统一的方式证明了许多已有的结论并得到更强的结果.在Trench工作的基础上,文[6]定义了k次R-对称矩阵,并指出对于任意奇异的Hermitian矩阵A,都存在k次单位矩阵R     

Delay nonlinear boundary conditions as limit of reactions concentrating in the boundary

In this work, we are interested in the dynamic behavior of a parabolic problem with nonlinear boundary conditions and delay in the boundary. We construct a reaction–diffusion problem with delay in the interior, where the reaction term is concentrated in a neighborhood of the boundary and this neighborhood shrinks to boundary, as a parameter ? goes to zero. We analyze the limit of the solutions of this concentrated problem and prove that these solutions converge in certain continuous function spaces to the unique solution of the parabolic problem with delay in the boundary. This convergence result allows us to approximate the solution of equations with delay acting on the boundary by solutions of equations with delay acting in the interior and it may contribute to analyze the dynamic behavior of delay equations when the delay is at the boundary.     

ASYMPTOTIC BEHAVIOR FOR A CLASS OF ELLIPTIC EQUIVALUED SURFACE BOUNDARY VALUE PROBLEM WITH DISCONTINUOUS INTERFACE CONDITIONS

Spontaneous potential well-logging is one of the important techniques in petroleum exploitation. A spontaneous potential satisfies an elliptic equivalued surface boundary value problem with diseontinuous interface conditlons. In practice, the measuring electrode is so small that we can simplify the corresponding equivalued surface to a point. In this paper, we give a positive answer to this approximation process: when the equivalued surface shrinks to a point, the solution of the original equivalued surface boundary value problem converges to the solution of the corresponding limit boundary value problem.     

一类两点边值问题正解的个数

讨论边值问题（（一v＇（r））~n）＇=λ（v~α＋v~β）,v＇（0）=v（1）=0,其中λ〉0是正参数.对（n-α）（n-β）〉0的情形得出了正解的存在唯一性.对0〈α〈n〈β的情形得到,存在λ~＊〉0,使得当0〈λ〈λ~＊时,此边值问题恰好存在两个正解;当λ=λ~＊时,此边值问题存在唯一一个正解;当λ〉λ~＊时,此边值问题不存在正解.     

THE BOUNDARY VALUE PROBLEMS FOR QUASILINEAR HIGHER ORDER ELLIPTIC EQUATIONS WITH A SMALL PARAMETER

In this paper we deal with the general boundary value problems for quasilinear higherorder elliptic equations with a small parameter before higher derivatives.By using themethod of multiple scales,we have proved that if the solution of degenerated boundary valueproblem exists,then under certain assumptions as the small parameter is sufficiently small,the solution of the origional boundary value problem exists as well and it is unique in a certainfunction space.Besides,the asymptotic expansion of the solution has been constructed.     

p-Laplace型非线性泛函差分方程正解的存在性

作者研究下述的p-Laplace型非线性泛函差分方程边值问题正解和多重正解的存在性,得到相应的充分条件,其中Φp(u)=|u|p-2u,P>1,(?)(0)= 0,C+={(?):(?)∈ C,(?)(k)≥0,k∈[-r,0])．     

Solutions to the $\sigma_k$-Loewner-Nirenberg Problem on Annuli are Locally Lipschitz and Not Differentiable

We show for $k \geq 2$ that the locally Lipschitz viscosity solution to the $\sigma_k$-Loewner-Nirenberg problem on a given annulus $\{a < |x| < b\}$ is $C^{1,\frac{1}{k}}_{\rm loc}$ in each of $\{a < |x| \leq \sqrt{ab}\}$ and $\{\sqrt{ab} \leq |x| < b\}$ and has a jump in radial derivative across $|x| = \sqrt{ab}$. Furthermore, the solution is not $C^{1,\gamma}_{\rm loc}$ for any $\gamma > \frac{1}{k}$. Optimal regularity for solutions to the $\sigma_k$-Yamabe problem on annuli with finite constant boundary values is also established.