某些非线性积分不等式

本文考虑一定有序局部紧空间上的非线性积分不等式，并给出其对于一定非线性积分方程的应用．     

一个非线性边值问题整体解的不存在性

本文对一类非线性偏微分方程的非线性边界问题作讨论，指出当满足一定条件时，该问题的解在有限时间内爆破，并给出一个时间估计。本文推广了Ｎ．Ｗｏｌａｎｓｋｉ在文［３］的结果。问题如下：     

非线性阻尼非线性刚度隔振系统随机动力学特性研究

针对随机激励环境,同时引入刚度和阻尼非线性来提高隔振系统的隔振性能.刚度和阻尼非线性分别是由水平弹簧和水平阻尼的几何布置获得.通过求解Fokker-Planck-Kolmogorov(FPK)方程等效非线性随机振动方程来研究非线性隔振系统在随机激励下的隔振性能,并使用路径积分和Monte-Carlo数值方法进行验证.在此基础上研究刚度非线性和阻尼非线性对隔振系统在随机激励下力传递率及其概率分布的影响.研究表明随着噪声强度的增加,非线性阻尼抑制振动的能力增强,但是在较小的随机激励下线性阻尼优于非线性阻尼.     

广义非线性模型的影响分析

本文从几何的观点研究广义非线性模型及其影响分析，我们给出了均值漂移模型的曲率度量；在此基础上，导广义非线性模型度量影响的诊断统计量的二阶近似公式，作为推论，本文的结果适用于两种重要的特殊情形，第一，广义线性模型的影响分析，第二，正态非线性模型的影响分析。     

非线性椭圆型Haseman边值问题

本文首先给出多个未知复函数的非线性椭圆型复方程组织的非线性Ｈａｓｅｍａｎ边值问题解的估计式，然后使用Ｌｅｒａｙ-Ｓｃｈａｕｄｅｒ定理讨论上述问题的可解性。     

具有非线性控制函数的概率收缩

本文引进具有非线性控制函数的概率收缩概念，在ＰＮ空间建立几个非线性算子方程解的存在唯一性定理，推广了Ａｌｔｍａｍ［１］和文献［５］的相应结果。     

层状复合材料结构边缘效应非线性分析

本文针对Ｐｉｐｅｓ－Ｐａｇａｎｏ均匀受拉模型，建立了几何非线性的准三维有限元模式。对四层对称铺设层板，得到了层间应力分布，并证实了边缘效应的存在性。线性与非线性结构表明，对角铺设层板，几何非线性的存在，在一定程度上缓和了边界层内的正应力集中，但对正交层板影响并不明显。     

非线性Robin边值问题的奇摄动

本应用微分不等式的方法，研究非线性Robin边值问题：     

非线性微分系统的Lipschitz稳定性

本文主要拓展Ｄａｎｎａｎ和Ｅｌｚｙｄｉ＾［１］提出的一致Ｌｉｐｓｃｈｉｔｚ稳定性概念，然后系统地研究了非线性微分系统的Ｌｉｐｚｈｉｔｚ稳定性，并应用于确定非线性系统的周期解问题，获得了一系列有意义的结果。     

n阶非线性微分方程的非线性三点边值问题

本文利用广义对接方法,建立了n阶非线性微分方程y(n)=f(x,y,y',…, y(n-1))满足非线性三点边界条件的非线性三点边值问题解的存在性与唯一性定理,所得结果将已有的很多相应结果作为特例.     

非线性期望和非线性估价的次可加性

证明了在适当的条件下F-期望的次可加性蕴涵条件F-期望的次可加性,F-估价的次可加性蕴涵Ft-相容非线性估价的次可加性.     

Nonlinear Lagrangians for Nonlinear Programming Based on Modified Fischer-Burmeister NCP Functions

This paper proposes nonlinear Lagrangians based on modified Fischer-Burmeister NCP functions for solving nonlinear programming problems with inequality constraints. The convergence theorem shows that the sequence of points generated by this nonlinear Lagrange algorithm is locally convergent when the penalty parameter is less than a threshold under a set of suitable conditions on problem functions, and the error bound of solution, depending on the penalty parameter, is also established. It is shown that the condition number of the nonlinear Lagrangian Hessian at the optimal solution is proportional to the controlling penalty parameter. Moreover, the paper develops the dual algorithm associated with the proposed nonlinear Lagrangians. Numerical results reported suggest that the dual algorithm based on proposed nonlinear Lagrangians is effective for solving some nonlinear optimization problems.     

Degenerate Nonlinear Boundary Value Problems for Fully Nonlinear Elliptic Equations of Second Order

In this paper, we will consider the degenerate nonlinear boundary value problems for nonlinear elliptic equations. We extend Lieberman & Trudinger's results from nondegenerate oblique derivative boundary values to degenerate boundary values.     

非线性评估方法研究

研究了评估中评价指标间的非线性特征对评估的影响,提出了对非线性特征明显的因素进行修正的方法和思路,最后针对院校实验室评估进行应用举例.     

Nonlinear Diffusion Processes

We study elliptic systems of strongly nonlinear first-order differential equations in complex form on the plane. For such systems we develop the theory of Hilbert boundary value problems which is very much similar to the well-known theory for a holomorphic vector. Systems of nonlinear elliptic equations describe problems of interaction of several nonlinear stationary processes in the diffusive and convective mass and heat transport by hydrodynamic fluid flows.     

Generalized Nonlinear Lagrangian Formulation for Bounded Integer Programming

Several nonlinear Lagrangian formulations have been recently proposed for bounded integer programming problems. While possessing an asymptotic strong duality property, these formulations offer a success guarantee for the identification of an optimal primal solution via a dual search. Investigating common features of nonlinear Lagrangian formulations in constructing a nonlinear support for nonconvex piecewise constant perturbation function, this paper proposes a generalized nonlinear Lagrangian formulation of which many existing nonlinear Lagrangian formulations become special cases.     

n阶非线性常微分方程的非线性两点边值问题

本文利用打靶法,给出了ｎ阶非线性常微分方程具有非线性两点边界条件的边值问题存在解与存在唯一解的一般性结果,并将所得结果应用于Ｌｉｐｓｃｈｉｔｚ方程的两点过值问题,给出了存在解与存在唯一解的具体的充分条件。     

Doubly Nonlinear Degenerate Parabolic Systems with Coupled Nonlinear Boundary Conditions

In this paper, we study the global existence and the global nonexistence of doubly nonlinear degenerate parabolic systems with nonlinear boundary conditions. We first prove a local existence result by the regularization method. Next, we construct a weak comparison principle. Then we discuss the large time behavior of solutions by using a modified upper and lower solution methods and constructing various upper and lower solutions. Necessary and sufficient conditions on the global existence of all positive (weak) solutions are obtained.     

多约束非线性整数规划的一种改进的算法

多约束非线性整数规划是一类非常重要的问题,非线性背包问题是它的一类特殊而重要的问题.定义在有限整数集上极大化一个可分离非线性函数的多约束最优化问题.这类问题常常用于资源分配、工业生产及计算机网络的最优化模型中,运用一种新的割平面法来求解对偶问题以得到上界,不仅减少了对偶间隙,而且保证了算法的收敛性.利用区域割丢掉某些整数箱子,并把剩下的区域划分为一些整数箱子的并集,以便使拉格朗日松弛问题能有效求解,且使算法在有限步内收敛到最优解.算法把改进的割平面法用于求解对偶问题并与区域分割有效结合解决了多约束非线性背包问题的求解.数值结果表明了改进的割平面方法对对偶搜索更加有效.