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相似文献   

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.     

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。     

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.     

非线性特征值问题正解的全局分歧

讨论非线笥特征值问题正解的全局分歧,即关于方程ｕ＝Ｆ（λ,ｕ）的分歧,其中ｕ限制在锥上,Ｆ（λ,．）按由锥诱导的序为正;给出了分歧存在的必要和充分条件及分歧枝的全局结构,并将所得到的结论应用到一个半线性椭圆型方程组中去。     

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.     

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.     

General nonlinear self-adjoint eigenvalue problem for systems of ordinary differential equations

The general nonlinear self-adjoint eigenvalue problem for systems of ordinary differential equations is considered. A method is proposed for reducing the problem to one for a Hamiltonian system. Results for Hamiltonian systems previously obtained by the authors are extended to this system.     

A Fixed Point Operator for a Nonlinear Boundary Value Problem

We study a semilinear second order equation with a nonlinear boundary condition for the axial deformation of a nonlinear elastic beam in the presence of friction. Under appropriate conditions we define a fixed point operator in order to obtain solutions for this equation.     

Exponentially convergent parallel algorithm for nonlinear eigenvalue problems

A. V. Klimenko, V. L. Makarov ^{A new algorithm for nonlinear eigenvalue problems is proposed.The numerical technique is based on a perturbation of the coefficientsof differential equation combined with the Adomian decompositionmethod for the nonlinear part. The approach provides an exponentialconvergence rate with a base which is inversely proportionalto the index of the eigenvalue under consideration. The eigenpairscan be computed in parallel. Numerical examples are presentedto support the theory. They are in good agreement with the spectralasymptotics obtained by other authors.}