非线性特征值问题平移对称幂法的收敛率估计

平移对称幂法（SS-HOPM）在求解源自玻色-爱因斯坦凝聚态的非线性特征值问题时,不仅具有较高的计算效率,而且具有点列收敛性,但其收敛率尚未得到有效估计.本文通过将多项式Kurdyka-Łojasiewicz（K-Ł）指数界的相关结果应用到所涉及优化问题的Lagrange函数上,得到了平移对称幂法的次线性收敛率估计,从理论上解释了平移对称幂法的计算效率.     

四阶非线性特征值问题正解的存在性

利用Krasnoselskii不动点定理,证明了边值问题y(4)(x)-λa(x)f(y(x))=0,O相似文献   

三阶非线性特征值问题解的存在性

利用锥不动点指数研究了三阶非线性特征值问题u+ρ3u=λg(t)f(u),00.     

非线性特征值问题的正解

本文着重考察非线性特征值问题u"+λg(t)f(u)=0,0＜t＜1,u(0)=u(1)=0,在没有任何单调性条件下,运用不动点指数理论,得到了上述问题的正解,推广、改进了以往的工作.     

非线性特征值问题的正解

本文着重考察非线性特征值问题u"+λg(t)f(u)=0, 0相似文献   

三阶非线性特征值问题的无穷多个正解

借助于Krasnosel'skii锥拉伸与锥压缩不动点定理研究了一类非线性三阶特征值问题无穷多个正解的存在性.     

一类张量特征值互补问题

矩阵特征值互补问题在力学系统领域有广泛的应用.在本文中,我们提出了一类特殊的四阶张量特征值互补问题,它是矩阵特征值互补问题的推广.我们对该特征值互补问题解的存在性,计算复杂度等性质进行了初步的研究.在一定条件下,我们建立了该互补问题同一类非线性约束优化问题的等价性联系,并由此提出了平移投影幂法来求解该特征值互补问题.     

关于非线性特征值问题的一个正解存在定理

本文利用锥上的Krasnosel‘ skii不动点定理考察了一类非线性特征值问题，获得了这个问题的一个正解存在定理。     

非线性特征值问题正解的存在性

证明了四阶边值问题y(4) =λα( x) f ( y( x) ) ,　 0 0且充分小时正解的存在性 .其中 ,α:[0 ,1 ]→ R连续 ,f ( 0 ) >0 .本文的工具是L eray- Schauder不动点定理 [4] .     

四阶非线性特征值问题的正解

本文考虑了四阶非线性特征值问题d4u/dt4=λg(t)f(u,u″),0＜t＜1,u(0)=u(1)=0,au″(0)-bu″′(0)=0,cu″(1)+du″′(1)=0.其中g(t)∈C((0,1),[0,∞)),f(u,v)∈C([0,∞)×(-∞,0],[0,∞)),a≥0,b≥0,c ≥0,d ≥ 0,且△=ac+ad+bc＞0.利用锥压缩与拉伸不动点定理,获得了上述问题正解的存在性结果.     

CONVERGENCE ANALYSIS ON SS-HOPM FOR BEC-LIKE NONLINEAR EIGENVALUE PROBLEMS

Shifted symmetric higher-order power method (SS-HOPM) has been proved effective in solving the nonlinear eigenvalue problem oriented from the Bose-Einstein Condensation (BEC-like NEP for short) both theoretically and numerically. However, the convergence of the sequence generated by SS-HOPM is based on the assumption that the real eigenpairs of BEC-like NEP are finite. In this paper, we will establish the point-wise convergence via Lojasiewicz inequality by introducing a new related sequence.     

Fixed point strategies for elastostatic frictional contact problems

Several fixed point strategies and Uzawa algorithms (for classical and augmented Lagrangian formulations) are presented to solve the unilateral contact problem with Coulomb friction. These methods are analysed, without introducing any regularization, and a theoretical comparison is performed. Thanks to a formalism coming from convex analysis, some new fixed point strategies are presented and compared with known methods. The analysis is first performed on continuous Tresca problem and then on the finite dimensional Coulomb problem derived from an arbitrary finite element method. Copyright © 2007 John Wiley & Sons, Ltd.     

Convergence analysis of generalized nonlinear inexact Uzawa algorithm for stabilized saddle point problems

This paper deals with a modified nonlinear inexact Uzawa (MNIU) method for solving the stabilized saddle point problem. The modified Uzawa method is an inexact inner-outer iteration with a variable relaxation parameter and has been discussed in the literature for uniform inner accuracy. This paper focuses on the general case when the accuracy of inner iteration can be variable and the convergence of MNIU with variable inner accuracy, based on a simple energy norm. Sufficient conditions for the convergence of MNIU are proposed. The convergence analysis not only greatly improves the existing convergence results for uniform inner accuracy in the literature, but also extends the convergence to the variable inner accuracy that has not been touched in literature. Numerical experiments are given to show the efficiency of the MNIU algorithm.     

Fixed point theorems in piecewise continuous function spaces and applications to some nonlinear problems

The piecewise continuous function space is an important state space in various nonlinear problems. In this paper, we establish some new fixed point theorems for the perturbed contraction operators in piecewise continuous function spaces. Our results can be applied to various integral operators. Some previous results are improved in this literature. As applications, the existence and uniqueness of solutions of impulsive anti‐periodic boundary value problems and the Lasota–Wazewska models with delays are exhibited at last two sections. Copyright © 2013 John Wiley & Sons, Ltd.     

Fixed point results on metric-type spaces

In this paper we obtain fixed point and common fixed point theorems for self-mappings defined on a metric-type space, an ordered metric-type space or a normal cone metric space. Moreover, some examples and an application to integral equations are given to illustrate the usability of the obtained results.     

不动点大类与 Nielsen数

通过引进 π１ （ Ｘ,ｘ０ ） 的同态 ｆπ 的不动子群 Ｆｉｘｆπ,在 Ｈ ＝ Ｆｉｘｆπ ·ｋｅｒｆ π为π１ （ Ｘ,ｘ０ ） 的正规子群时定义了不动点大类,得到不动点大类数是有限的．在曲面 Ｘ的正则复迭空间 Ｘ Ｈ 为有限叶时只要姜子 群相对于 Ｈ 极大,ｆ 的 Ｎｉｅｌｓｅｎ 数就可以用一维同调群计算