二阶常微分方程及Thomas－Fermi方程的边值问题

本文利用上、下解方法推广了Ｍ．Ｌｅｅｓ关于半线性边值问题的结果，给出了另一类边值问题解的存在唯一性的一个充分条件；并利用所得的结果证明了Ｔｈｏｍａｓ－Ｆｅｒｍｉ方程的边值问题解的存在唯一性，从而推广了Ｃ．ＤＬｕｎｉｎｇ的结果．     

二阶常微分方程及Thomas—Fermi方程的边值问题

本文利用上、下解方法推广了Ｍ．Ｌｅｅｓ关于半线性边值问题的结果，给出了另一类边值问题解的存在唯一性的一个充分条件；并利用所得的结果证明了Ｔｈｏｍａｓ－Ｆｅｒｍｉ方程的边值问题解的存在唯一性，从而推广了Ｃ．Ｄ．Ｌｕｎｉｎｇ的结果。     

线性Schrdinger方程的初边值问题(英文)

本文证明了非线性 Ｓｃｈｒｏｄｉｎｇｅｒ方程的初边值问题的 Ｈｓ－解（１＜ ｓ ≤ ２）的存在唯一性结果．     

Thomas－Fermi方程的孤立中性原子型边值问题

本文利用构造上、下解方法，研究奇异方程、（ｔ）Ｘ＇＇＝ｆ（ｔ，ｘ）的极限边值问题解的存在唯一性，证明了Ｔｈｏｍｓ－Ｆｅｒｍｉ方程对应于孤立中性原子型边值问题有唯一解，所得结果推广了Ａ．Ｍａｍｂｒｉａｎｉ定理     

Ginzburg-Landau-BBM方程的指数吸引子

本文利用挤压性质和算子分解方法证明了Ｇｉｎｚｂｕｒｇ－Ｌａｎｄａｕ－ＢＢＭ耦合方程组周期初边值问题指数吸引子的存在性．     

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．     

Thomas—Fermi方程的孤立中性原子型边值问题

本文利用构造上、下解方法、研究奇异方程ψ（ｔ）ｘ‘’＝ｆ（ｔ，ｘ）的极限边值问题解的存在唯一性，证明了Ｔｈｏｍｓ－Ｆｅｒｍｉ方程对应于孤立中性原子型边值问题有唯一解，所得结果推广了Ａ．Ｍａｍｂｒｉａｎｉ定理。     

广义Fitz－Hugh－Nagumo方程组的整体吸引子及惯性流形

本文考虑广义Ｆｉｔｚ－Ｈｕｇｈ－Ｎａｇｕｍｏ方程组的初边值问题．去掉解属于某不变区域的限制，我们证明了初值属于Ｌ２情形下整体吸引子的存在性，并给出其维数估计．对二维情形证明了其惯性流形的存在性．我们的方法简化了Ｐ．Ｃｏｎｓｔａｎｔｉｎ等人的工作．     

Klein-Gordon方程初达值问题的一个新的守恒差分格式

本文对非线性Klein－Gordon（NKG）方程的初边值问题提出了一种新的差分格式,它保持了NKG方程初边值问题的能量守恒．证明了该格式的收敛性和稳定性．特别地,由于该格式是完全隐式的,故对求长时解有着重要的作用．数值计算结果表明该方法计算速度快,精度好．     

Cahn-Hilliard方程的动力学稳定性

考虑Cahn－Hilliard方程且a2p-1＞0）的初边值问题,证明了系统在H1－H3中关于f系数的状动于H2中Hausdoorff半距离下稳定的全局吸引子的存在性．     

二阶非线性椭圆型方程带位移的边值问题

In this paper, we consider the boundary value problem with the shift for nonlinear uniformly elliptic equations of second order in a multiply connected domain. For this sake, we propose a modified boundary value problem for nonlinear elliptic systems of first order equations, and give a priori estimates of solutions for the modified boundary value problem. Afterwards we prove by using the Schauder fixedpoint theorem that this boundary value problem with some conditions has a solution. The result obtained is the generlization of the corresponding theorem on the Poincare boundary value problem.     

Universal boundary value problem for equations of mathematical physics

A new statement of a boundary value problem for partial differential equations is discussed. An arbitrary solution to a linear elliptic, hyperbolic, or parabolic second-order differential equation is considered in a given domain of Euclidean space without any constraints imposed on the boundary values of the solution or its derivatives. The following question is studied: What conditions should hold for the boundary values of a function and its normal derivative if this function is a solution to the linear differential equation under consideration? A linear integral equation is defined for the boundary values of a solution and its normal derivative; this equation is called a universal boundary value equation. A universal boundary value problem is a linear differential equation together with a universal boundary value equation. In this paper, the universal boundary value problem is studied for equations of mathematical physics such as the Laplace equation, wave equation, and heat equation. Applications of the analysis of the universal boundary value problem to problems of cosmology and quantum mechanics are pointed out.     

N阶m点非线性边值问题的三正解的特征值准则

应用算子特征值准则研究了一类高阶多点边值问题多重正解的存在性,其中非线性项满足Caratheodory条件.将特征值准则应用到n阶m点的非线性边值问题,并证明了微分方程至少三正解的存在性.     

取油管振动方程解的整体不存在性

讨论推广的海底取油管振动方程的初边值问题和初值问题解的整体不存在性,对初边值问题推广了Gmira和Guedda得到的结果,对初值问题的结果是新的.     

含有积分、反周期和带P-Laplacian算子的分数阶微分方程边值问题解的存在性

利用格林函数的性质和Banach压缩映射原理讨论了含P-Laplacian算子反周期边值问题的解.首先,求出与该边值问题相关的格林函数并给出了格林函数的性质;然后将边值问题转化为与其等价的积分方程,利用格林函数的性质及Banach压缩映射原理得到边值问题解的唯一性;最后给出实例验证结果的合理性.     

Boundary value problems for two types of degenerate elliptic systems in R~4

Firstly, the Riemann boundary value problem for a kind of degenerate elliptic system of the first order equations in R~4 is proposed. Then, with the help of the one-to-one correspondence between the theory of Clifford valued generalized regular functions and that of the degenerate elliptic system's solution, the boundary value problem as stated above is transformed into a boundary value problem related to the generalized regular functions in Clifford analysis. Moreover, the solution of the Riemann boundary value problem for the degenerate elliptic system is explicitly described by using a kind of singular integral operator. Finally, the conditions for the existence of solutions of the oblique derivative problem for another kind of degenerate elliptic system of the first order equations in R~4 are derived.     

Mixed Elastico-Plasticity Problems with Partially Unknown Boundaries

In this paper,we study mixed elastico-plasticity problems in which part of the boundary is known,while the other part of the boundary is unknown and is a free boundary.Under certain conditions,this problemcan be transformed into a Riemann-Hilbert boundary value problem for analytic functions and a mixed boundaryvalue problem for complex equations.Using the theory of generalized analytic functions,the solvability of theproblem is discussed.     

A novel method for solving a class of singularly perturbed boundary value problems based on reproducing kernel method

In this paper, a novel method is presented for solving a class of singularly perturbed boundary value problems. Firstly the original problem is reformulated as a new boundary value problem whose solution does not change rapidly via a proper transformation; then the reproducing kernel method is employed to solve the boundary value new problem. Numerical results show that the present method can provide very accurate analytical approximate solutions.     

Singular numbers of the monodromy operator and sufficient conditions of the asymptotic stability of periodic system of differential equations with fixed delay

To obtain sufficient conditions for the asymptotic stability of linear periodic systems with fixed delay commensurable with the period of coefficients, singular numbers of the monodromy operator are used. To find these numbers, a self-adjoint boundary value problem for ordinary differential equations is applied. We study the motion of eigenvalues of this boundary value problem under a variation of a parameter. Obtaining sufficient conditions for the asymptotic stability is reduced to finding the bifurcation value of the parameter for the boundary value problem.     

The Basic Mixed Problem for an Anisotropic Elastic Body

The mixed boundary value problem is considered for an anisotropic elastic body under the condition that a boundary value of the displacement vector is given on some part of the boundary and a boundary value of the generalized stress vector on the remainder. Using the potential method and the theory of singular integral equations with discontinuous coefficients, the existence of a solution of the mixed boundary value problem is proved.