The Hilbert Problem for the First Order Elliptic Complex Equation With Discontinuous Coefficients

本文研究一阶带间断系数的椭圆型复方程的Ｈｉｌｂｅｒｔ边值问题，在一定条件下给出了上述问题解的存在性、可解条件以及解的积分表示式．     

多连通区域上一阶椭圆型复方程的Riemann-Hilbert问题与其适定性

In this article, we first propose the Riemann-Hilbert problem for uniformly elliptic complex equations of first order and its well-posed-ness in multiply connected domains.Then we give the integral representation of solutions for modified Riemann-Hilbert problem of the complex equations. Moreover we shall obtain a priori estimates of solutions of the modified Riemann-Hilbert problem and verify its solvability. Finally the solvability results of the original boundary value problem can be obtained.     

Asymptotic and Oscillatory Behavior of Solutions of First Order Neutral Differential Equations

This paper has made researches on first order neutral differential equations with variable coefficients and several deviations. The asymptotic behavior of nonoscillatory solutions of the equations are discussed. Necessary and sufficient conditions and several sufficient conditions for the oscillations of the equations are obtained. The relevent results in [1—3] are improved and generalized .     

Equivalence of three kinds of well-posed-ness of discontinuous Riemann-Hilbert problem for elliptic complex equation in multiply connected domains

In this article, we first introduce the general linear elliptic complex equation of first order with certain conditions, and then propose discontinuous Riemann-Hilbert problem and some kinds of modified well-posed-ness for the complex equation. Then we verify the equivalence of three kinds of well-posed-ness. The discontinuous boundary value problem possesses many applications in mechanics and physics etc.     

Variational Regularization of the Inverse Problem of a Class of Nonlinear Time-Fractional Diffusion Equations北大核心CSCD

考虑了一类二维非线性时间分数阶扩散方程,并从最终位置获取的测量数据来反演物质在u(0, y, t)处的物理信息。这个问题是严重不适定的,即问题的解并不连续依赖于测量数据,因此提出了变分型正则化方法来稳定求解该问题。给出了精确解与正则近似解之间的误差估计,数值算例验证了该方法的有效性。     

Solvability of the Dirichlet Problem in W~（2,p ）for a Class of Elliptic Equations with Singular Data

We prove an existence and uniqueness result for the Dirichlet problem for a class of elliptic equations with singular data in weighted Sobolev spaces.     

A new process for constructing coefficients of elliptic complex equations in multiply connected domains

This article concerns the inverse problem for linear elliptic systems of first-order equations with Riemann–Hilbert-type map in multiply connected domains. First the formulation and the complex form of the problem for the systems are given, and then the coefficients of the elliptic complex equations for the above problem are constructed by a complex analytic method, where the advantage of the methods in other papers is absorbed, and the used method in this article is more simple and the obtained result is more general. As an application of the above results, we can derive the corresponding results of the inverse problem for second-order elliptic equations from Dirichlet to Neumann map in multiply connected domains.     

The oblique derivative problem for nonlinear elliptic complex equations of second order in multiply connected unbounded domains

In this article,we discuss that an oblique derivative boundary value problem for nonlinear uniformly elliptic complex equation of second order with the boundary conditions in a multiply connected unbounded domain D.The above boundary value problem will be called Problem P.Under certain conditions,by using the priori estimates of solutions and Leray-Schauder fixed point theorem,we can obtain some results of the solvability for the above boundary value problem(0.1) and(0.2).     

The mixed problem for degenerate elliptic equations of second order

The present paper deals with the mixed boundary value problem for elliptic equations with degenerate rank 0. We first give the formulation of the problem and estimates of solutions of the problem, and then prove the existence of solutions of the above problem for elliptic equations by the above estimates and the method of parameter extension. We use the complex method, namely first discuss the corresponding problem for degenerate elliptic complex equations of first order, afterwards discuss the above problem for degenerate elliptic equations of second order.     

Existence theory for first order discontinuous functional differential equations

We prove the existence of extremal solutions for a first order functional differential equation subject to nonlinear boundary conditions of functional type. Moreover, the functions that define our problem are allowed to be discontinuous. The proof of our main result is based on a generalized iterative technique.

     

Riemann-Hilbert problem for first order complex equations of mixed type with degenerate curve

This paper considers the Riemann-Hilbert problem for linear mixed（elliptichyperbolic） complex equations of first order with degenerate curve in a simply connected domain. We first give the representation theorem and uniqueness of solutions for such boundary value problem. Then by using the methods of successive iteration and parameter extension, the existence of solutions for this problem is proved.     

Periodic solutions for second order differential equations with discontinuous restoring forces

We deal with the existence of periodic solutions for problems with a jump discontinuity. We use an approximation procedure and the method of the lower and upper solutions.     

Oblique derivative problems for second order nonlinear equations of mixed type in multiply connected domains

In this paper, the unique solvability of oblique derivative boundary value problems for second order nonlinear equations of mixed (elliptic-hyperbolic) type in multiply connected domains is proved, which mainly is based on the representation of solutions for the above boundary value problem, and the uniqueness and existence of solutions of the above problem for the equation u_xx + sgn y u_yy = 0.     

Oblique derivative problems for nonlinear elliptic systems with measurable coefficients

1 Problem formulation Let Q be a bounded multiply connected domain in RN and the boundary OQ E C2. W6consider the nonlinear elliptic system of second order equationsUnder certain conditions, system (1) can be reduced to the formwhere u = (ul,' t u.), Da = (u..), DZu = (u:..,), andSuppose that (1) (or (2)) satisfiesCondition C For arbitrary functions u'(x), u'(z) E Cd(~) n W::(Q), Fk(x,u,Du,DZu)(k = 1,' I m) satisfy the conditionswhere 0 < g < 1, u == al - u2, and al:), bit), of*),…