Extremal Solutions of a Class of Nonlinear Integro-Differential Equations in Banach spaces

The monotone iterative technique is applied to a class of nonlinear first order integro-differential equations in Banach spaces. First a linear system with a ``small' nonlinear perturbation is solved using Banach's Contraction Principle and the technique of Green's function. Then based upon a comparison result, the existence of minimal and maximal solutions is proved.

     

二次曲面的几个性质

介绍了二次曲面的切线的几个性质 ,把二次曲线的类似性质推广到了二次曲面 .     

Iterative Solutions for a Non-monotone BinaryOperator Equations and Operator System of Equations

By using the theory of the cone and partial ordering. It is studied that the existence and uniqueness of solutions for a non-monotone binary operator equation A(x, x)= x and operator system of equations A(x,x)=x,B(x,x)=x in Banach spaces. Where A and B can be decomposed A=A1+A2, B=B1+B2,A1 and B1 are mixed monotone, A2 and B2 are anti-mixed monotone. The results presented here improve and generalize some corresponding results of mixed monotone operator equations.     

基于偏好锥的DEA-DA模型研究

扩展的DEA-DA模型是一种结合数据包络分析(DEA)和判别分析(DA)的非参数判别分析方法。一种锥比率DEA模型C^2WH可以利用锥比率体现决策对样本指标和决策单元的偏好。因此，本将C^2WH模型和DA模型结合，建立了基于偏好锥的DEA-DA模型与方法，并就偏好锥为多面凸锥的情况给出了实例分析。结果表明，所建模型可以在判别分析过程中体现决策的偏好，从而形成主观与客观的集成评价。     

Banach空间中非线性脉冲Volterra型积分方程组的可解性

在较弱的条件下，利用锥理论和单调迭代方法首先建立了Banach空间中一类非线性算子方程组最小最大解的存在性定理；然后作为应用，利用一个新的比较结果，得到了Banach空间中非线性脉冲Volterra型积分方程组的整体解，改进了最近的许多结果．     

二阶脉冲微方程三点边值问题解的存在性

We study the existence of solutions to the second order three-point boundary value problem: where 0 <η< 1, α∈R, and f : [0, 1]×R×R→R, Ii: R×R→R, Ji : R×R→R(i=1,2,…k) are continuous. Our results is new and different from previous results. In particular, we obtain the Green function of the problem, which makes the problem simpler.     

近似锥-次类凸集值优化问题的强有效性

利用凸集分离定理，得到了向量集值优化问题(VP)取得强有效解的Kuhn—Tucker型必要条件。在近似锥-次类凸假设下。得到了(VP)取得强有效解的充分条件。最后。在强有效意义下给出了与(VP)等价的两种无约束规划。     

Representation of the Clarke subdifferential for a regular quasidifferentiable function

A class of Lipschitz quasidifferentiable functions is described for which the exact representation of the Clarke subdifferential in terms of a quasidifferential holds. The sufficient conditions formulated are different from those previously established by Rubinov and Akhundov.     

四阶边值问题正解的存在性与多解性

本文讨论了非线性四阶边值问题u^(4)(t)=φ（t）f(u(t),u“(t),t∈(0,1),u(0)=u(1)=u“(0) =u“(1)=0正确的存在性，其中φ（t)∈C([0,1],[0,∞)),f(u,v)∈C（[0,∞],[0,∞))。利用锥压缩与锥拉伸不动点定理，给出了该问题正解存在与多个正解存在的充分条件。     

混合单调算子的不动点定理

引入了伴随列的概念，运用锥理论证明了一类混合单调算子存在不动点的充分必要条件。