一类新型"增"算子的不动点定理及应用

在σ-备线性半序空间和具有正规锥P的实Banach空间,分别讨论其假设条件和论证方法均与以往不同的新型"增"算子,获得多个不动点的存在性定理与存在唯一性定理,并应用于非线性扩散、气体点燃、生化浓缩等领域中非线性特征值问题的求解。     

一类常微分方程组正解的存在性

讨论了一类二、四阶耦合常微分方程组正解的存在性,利用不动点定理和度理论,在一定条件下得到了该方程组正解的两个存在性定理。     

非线性微分方程组边值问题多个正解的存在性

本文考虑了张力桥稳定性问题的数学模型,对相应的非线性微分方程组边值问题正解的存在性问题进行了研究.通过构造特殊的锥,在不同区间上利用锥拉伸和锥压缩不动点定理,给出了一类复合型非线性微分方程组边值问题一个或多个正解的存在性,并且给出几个例子说明本文定理的应用,从而有助于对实际工程中张力桥的稳定性问题的研究.     

带有多项分数阶导数的微分方程边值问题解的存在性

自然科学中的许多实际问题可以用分数阶微分方程模型来描述,并且分数阶微积分和分数阶微分方程已经成为处理某些实际问题的重要数学工具。利用压缩映象原理、Krasnoselskii不动点定理和非紧测度理论研究一类带有混合边值条件的分数阶微分方程,并获得了非线性项在满足不同的条件下方程解的存在性和唯一性结果。这些结果推广了经典的 Bagley-Torvik 方程及相关模型解的存在性定理。     

Elementary solutions of coupled model equations in the kinetic theory of gases

The method of elementary solutions is employed to solve two coupled integrodifferential equations sufficient for determining temperature-density effects in a linearized BGK model in the kinetic theory of gases.Full-range completeness and orthogonality theorems are proved for the developed normal modes and the infinite-medium Green's function is constructed as an illustration of the full-range formalism.The appropriate homogeneous matrix Riemann problem is discussed, and half-range completeness and orthogonality theorems are proved for a certain subset of the normal modes. The required existence and uniqueness theorems relevant to the H matrix, basic to the half-range analysis, are proved, and an accurate and efficient computational method is discussed. The half-space temperature-slip problem is solved analytically. and a highly accurate value of the temperature-slip coefficient is reported.     

Almost periodic solutions for impulsive fractional differential equations

In this paper, we consider the existence of almost periodic solutions for impulsive fractional evolution equations involving Caputo fractional derivative. The main results are obtained by means of the theory of operators semi-group, probability density functions, fixed point theorems and the techniques based on fractional calculus. An example is also discussed to illustrate the theory. Some known results are improved and generalized.     

非线性分数阶耦合泛函微分方程组边值问题的可解性

由于运动速度是有限的，因此在信号传输等过程中时滞现象往往是不可避免的。分数阶泛函微分方程是研究时滞系统运动规律的重要模型，当系统中具有两个或多个状态变量且这些状态变量相互作用时，常常运用耦合微分方程组来刻画。对一类具有 Riemann-Liouville 分数阶导数的非线性时滞耦合泛函微分方程组边值问题正解的存在唯一性进行了研究。首先，根据方程与边界条件的特点，建立了比较定理，构造了上解与下解的单调序列，并确定了上下解的关系。运用上下解的方法建立并证明了边值问题正解的存在性定理，同时得到了正解的取值范围。然后，利用迭代技术建立并证明了边值问题正解的存在唯一性定理。最后，给出了具体例子用于说明所得主要结论的适应性与广泛性。     

Numerical inclusion methods of solutions for variational inequalities

We consider a numerical method that enables us to verify the existence of solutions for variational inequalities. This method is based on the infinite dimensional fixed point theorems and explicit error estimates for finite element approximations. Using the finite element approximations and explicit a priori error estimates, we present an effective verification procedure that through numerical computation generates a set which includes the exact solution. Copyright © 2002 John Wiley & Sons, Ltd.     

四阶奇异边值问题的正解

利用了上下解方法和不动点定理，得到了一类四阶奇异边值问题正解的存在性。     

A note on the existence and uniqueness of solutions of the micropolar fluid equations

We show that existence and uniqueness theorems, known in the theory of the Navier-Stokes equations, are valid for the incompressible micropolar equations too.     

Banach空间半直线上奇异脉冲积分-微分方程初值问题解的存在性和唯一性

本文在更广泛的情况下,利用Sadovskii不动点定理研究了Banach空间中半直线上一类非线性奇异脉冲积分-微分方程初值问题解的存在性和唯一性,推广并改进了已有文献中的相关结果。     

Banach空间一类奇异脉冲微分方程的边值问题

讨论了Banach空间中一类具有奇异性的脉冲微分方程的边值问题，利用Moench不动点定理，获得了该边值问题的存在性，并给出在无穷维奇异脉冲微分方程组中的应用。     

一类捕食——食饵模型正解的存在唯一性与稳定性

本文主要研究一类具有非单调生长率的捕食食饵模型的平衡态正解问题．首先通过计算锥上紧算子的不动点指标,得到了正解存在的充分条件;其次,运用线性算子扰动理论以及拓扑度理论,讨论了参数对于正解唯一性与线性稳定性的影响;最后,通过数值模拟分别验证了在一维空间和二维空间下正解的存在性结论,也就是捕食者和食饵在一定条件下可以共存．     

Banach空间中非线性混合型脉冲积分-微分方程初值问题的解

研究了Banach空间中非线性脉冲积分-微分方程初值问题解的存在性。在比较宽松的紧性条件下,利用Mnch不动点定理,通过引进等价范数,递归法和拟幂零算子,建立了新的存在性定理,推广和改进了于立新和刘立山在2003所建立的相关结果。     

Adaptive modification of objective function for lagrange multiplier method in constrained optimization problems

Abstract

This paper proposes an adaptive modification method to transform the objective function with a stationary point to an objective function with a minima point, such that search methods can be used to find the stationary point. The stationary point can be a saddle point in addition to a minima or a maxima. Therefore, this method can be used to transform a constrained optimization by applying Lagrange multipliers to an unconstrained optimization problem. A quadratic term, ½(X — X_N ) ^{T D} (X—X_N ), is added to the original function such that the modified function is a minima at the Newton point X_N of the original function, where D is a diagonal matrix to make the modified Hessian matrix H_O + D positive definite, and H_O is the original Hessian matrix at the initial point X_O .     

The coupled theory of micropolar thermoelastic diffusion

The general equations of motion and constitutive equations are derived for a general homogeneous anisotropic medium with a microstructure, taking into account the effects of heat and diffusion. We establish a reciprocal relation, which involves two thermoelastic diffusion processes at different instants. We show that this relation can be used to obtain reciprocity, uniqueness and continuous dependence theorems. The reciprocity theorem avoids both the use of the Laplace transform and the incorporation of initial conditions into the equations of motion. The uniqueness theorem is derived without the positive definiteness assumption on the elastic, conductivity and diffusion tensors. We prove also that the reciprocal relation leads to a continuous dependence theorem studied on external body loads. Finally we prove the existence of a generalized solution by means of the semigroup of linear operators theory.     

Plane interior boundary-value problems in microcontinuum fluid mechanics

This paper examines the fundamental question of existence and uniqueness of solutions of two plane interior boundary-value problems encountered in the field of microcontinuum fluid mechanics. These problems are analyzed using potential theoretic methods and with the aid of singular integral equations. The results obtained have their counterparts in the classical Navier-Stokes theory.     

二阶常微分方程周期边值问题的正解

非线性二阶周期边值问题可描述天体力学、工程和生物中出现的许多周期现象,其广泛的应用引起了许多学者的关注.本文主要研究二阶周期边值问题正解的存在性,其中非线性项包含一阶导数项.设非线性项满足Caratheodory条件,利用零点指数理论和分析技巧,本文建立了二阶周期边值问题正解的存在性定理,推广并改进了一些已知结果.最后给出一个例子说明主要结果.     

On the theory of heat conduction in micromorphic continua

The paper is concerned with the linear theory of heat conduction in micromorphic continua. First, a study of boundary-value problems of the stationary theory is presented. A representation of Galerkin type is established and fundamental solutions are derived. The potentials of single layer and double layer are used to reduce the boundary-value problems to singular integral equations. Existence and uniqueness results are established. The second part of the paper is devoted to non-stationary thermal fields. A continuous dependence result and an existence theorem are presented.