On singular perturbations of superlinear elliptic systems

We study the existence, multiplicity and shape of positive solutions of the system −ε²Δu+V(x)u=K(x)g(v), −ε²Δv+V(x)v=H(x)f(u) in RN, as ε→0. The functions f and g are power-like nonlinearities with superlinear and subcritical growth at infinity, and V, H, K are positive and locally Hölder continuous.     

Endpoint estimates for some maximal operators associated to the circular conical surface

For and m>0 we consider the maximal operator given by

     

Maximal commutators of BMO functions and singular integral operators with non-smooth kernels on spaces of homogeneous type

Let X be a space of homogeneous type in the sense of Coifman and Weiss. In this paper, via a new Cotlar type inequality linking commutators and corresponding maximal operators, a weighted Lp(X) estimate with general weights and a weak type endpoint estimate with A₁(X) weights are established for maximal operators corresponding to commutators of BMO(X) functions and singular integral operators with non-smooth kernels.     

A semi-analytic solution for multiple curved cracks emanating from circular hole using singular integral equation

This paper provides an elastic solution for an infinite plate containing multiple curved edge cracks emanating from a circular hole. A fundamental solution is suggested, which represents a particular solution for a concentrated dislocation in an infinite plate with the traction free hole. The generalized image method and the concept of the modified complex potentials are used in the derivation of the fundamental solution. After using the fundamental solution and placing the distributed dislocations at the prospective sites of cracks, a singular integral equation is formulated. The singular integral equation is solved by using the curve length method in conjunction with the semi-opening quadrature rule. By taking an additional point dislocation at the hole center, the number of the unknowns is equal to the number of the resulting algebraic equations. This is a particular advantage of the suggested method. Finally, several numerical examples are given to illustrate the efficiency of the method presented. Numerical examinations are carried out and sufficient accurate results have been found.     

Solving integro-differential equations with Cauchy kernel

A simple method for solving the Fredholm singular integro-differential equations with Cauchy kernel is proposed based on a new reproducing kernel space. Using a transformation and modifying the traditional reproducing kernel method, the singular term is removed and the analytical representation of the exact solution is obtained in the form of series in the new reproducing kernel space. The advantage of the approach lies in the fact that, on the one hand, by improving the definition of traditional inner product, the representation of new reproducing kernel function becomes simple and requirement for image space of operator is weakened comparing with traditional reproducing kernel method; on the other hand, the approximate solution and its derivatives converge uniformly to the exact solution and its derivatives. Some examples are displayed to demonstrate the validity and applicability of the proposed method.     

Elliptic polynomials orthogonal on the unit circle with a dense point spectrum

We introduce two explicit examples of polynomials orthogonal on the unit circle. Moments and the reflection coefficients are expressed in terms of the Jacobi elliptic functions. We find explicit expression for these polynomials in terms of elliptic hypergeometric functions. We show that the obtained polynomials are orthogonal on the unit circle with respect to a dense point measure. We also construct corresponding explicit systems of polynomials orthogonal on the interval of the real axis with respect to a dense point measure. They can be considered as an elliptic generalization of the Askey-Wilson polynomials of a special type.      

具p-Laplacian算子型奇异边值问题的正解

考虑一类p-Laplacian算子型泛函微分方程的奇异边值问题,利用锥不动点定理,得到了其正解及多个正解存在的充分条件．     

薄层流中的一类三阶奇摄动边值问题的渐近分析

本文研究薄层流中出现的一类三阶奇摄动数学模型．本文不采用研究其渐近等价的二阶奇摄动微分方程的方法,而利用边界层函数法,直接讨论该数学模型的渐近解,并严格地证明了解的存在唯一性和其渐近解的一致有效性．本文的结果不仅去掉了以往方法所必须的位势条件,纠正了某个不适定的假设,而且推广了以往的结果．     

JACOBI PSEUDOSPECTRAL METHOD FOR FOURTH ORDER PROBLEMS

In this paper, we investigate Jacobi pseudospectral method for fourth order problems. We establish some basic results on the Jacobi-Gauss-type interpolations in non-uniformly weighted Sobolev spaces, which serve as important tools in analysis of numerical quadratures, and numerical methods of differential and integral equations. Then we propose Jacobi pseudospectral schemes for several singular problems and multiple-dimensional problems of fourth order. Numerical results demonstrate the spectral accuracy of these schemes, and coincide well with theoretical analysis.     

具时变时滞和 Markovian转换的不确定奇异随机系统的鲁棒 H_∞ 滤波(英文)

本文处理了一类具与模式有关的时变时滞和 Markovian转换的不确定奇异随机系统的鲁棒H∞滤波问题.所考虑的系统包含参数不确定性,Markovian参数,随机扰动和与模式有关的时变时滞.本文的目的是设计一个滤波器以保证滤波错误系统是正则的、无脉冲的、鲁棒指数均方稳定的和可达到一个给定的 H∞扰动衰减水平.文章首先得到所求鲁棒指数H∞滤波器存在的充分条件,然后给出所求滤波器参数的显示表示.