椭圆系统的正解(英文)

本文主要研究在一些假设条件下拟线性方程组div(|▽ui|pi-2▽ui)+λki(|x|).fi(u1,…,un)=0,pi>1,i=1,…,n在环状区域径向正解的存在性及多重性.我们主要应用锥内的不动点定理.     

非线性奇异弹性梁方程组正解的存在性

利用不动点理论, 通过构造特殊的锥, 研究了弹性梁方程组正解的存在性. 最后, 通过具体的例子说明了主要结果的有效性.     

四阶奇异边值问题的正解

该文利用锥不动点理论，分别给出了超线性四阶微分方程奇异边值问题正解存在的充分条件和充分必要条件.     

非线性参数椭圆系统正解的存在性与多解性

本文讨论了一类非线性含参数椭圆系统正解的存在性与多解性,通过线性算子的谱半径,给出其正径向解存在与多解的条件,本质上改进和推广了文[1－3]的结果．     

An algorithm based on resolvent operators for solving variational inequalities in Hilbert spaces

In this paper, a new monotonicity, M$M$-monotonicity, is introduced, and the resolvent operator of an M$M$-monotone operator is proved to be single valued and Lipschitz continuous. With the help of the resolvent operator, an equivalence between the variational inequality VI(C,F+G)$(C,F+G)$ and the fixed point problem of a nonexpansive mapping is established. A proximal point algorithm is constructed to solve the fixed point problem, which is proved to have a global convergence under the condition that F$F$ in the VI problem is strongly monotone and Lipschitz continuous. Furthermore, a convergent path Newton method, which is based on the assumption that the projection mapping _∏C(⋅)${\prod }_C(\cdot )$ is semismooth, is given for calculating ε$\epsilon$-solutions to the sequence of fixed point problems, enabling the proximal point algorithm to be implementable.     

一类非线性算子方程的多重正解及其应用

本文利用不动点指数理论对一类非线性算子方程建立了多重正解的存在性定理，并将所获结果应用到Ｈａｍｍｅｒｓｔｅｉｎ积分方程和Ｓｔｕｒｍ Ｌｉｏｕｖｉｌｅ两点边值问题，得到了新的结论，本质上改进和推广了［２，４，５，６，８－１２］的工作．     

Weak type estimates on certain Hardy spaces for smooth cone type multipliers

Let ?n∈C^∞(Rd?{0}) be a non-radial homogeneous distance function of degree n∈N satisfying ?n(tξ)=tn?n(ξ). For f∈S(Rd+1) and δ>0, we consider convolution operator associated with the smooth cone type multipliers defined by

     

排水粉喷桩(2D工法)加固软土地基对桩周土体强度的影响

排水粉喷桩(简称2D工法)作为一种新的软土地基处理方法,在淮盐公路软基处理中得到试用,效果良好;但是目前对其桩间土强度的变化规律还不是很清楚,本文首次通过大量现场试验,采用静力触探、十字板剪切等试验手段,测得了排水粉喷桩施工后桩间土强度变化的规律。结果显示在排水粉喷桩施工后,桩间土强度先降低,之后随着龄期的增长而提高。