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Existence of solutions for sub-linear or super-linear operator equations

Science China Mathematics 2015年第8期58卷 1653-1664页

作者： CHEN YingYing DONG YuJun SHAN Yuan Department of Mathematics Nanjing Normal University Department of Mathematics Nanjing University

We investigate solutions to superlinear or sublinear operator equations and obtain some abstract existence results by minimax methods. These results apply to superlinear or sublinear Hamiltonian systems satisfying several boundary value conditions including Sturm-Liouville boundary value conditions and generalized periodic boundary value conditions, and yield some new theorems concerning existence of solutions or nontrivial solutions. In particular, some famous results about periodic solutions to superlinear or sublinear Hamiltonian systems by Rabinowitz or Benci and Rabinowitz are special cases of the theorems.

关键词： superlinear sublinear operator equations existence of solutions minimax methods Hamiltoniansystems

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MULTILEVEL AUGMENTATION METHODS FOR SOLVING operator equations

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Numerical Mathematics(Theory,Methods and Applications) 2005年第1期 31-55页

作者：陈仲英巫斌许跃生 Academy of Mathematics and System Sciences Beijing 100080 Chinese Academy of Sciences Department of Mathematics Department of Scientific Computing and Computer Applications Department of Scientific Computing and computer Applications Guangzhou 510275 NY 13244-1150 PRC. Syracuse University USA/ Institute of Mathematics Zhongshan University

We introduce multilevel augmentation methods for solving operator equations based on direct sum decompositions of the range space of the operator and the solution space of the operator equation and a matrix splitting scheme. We establish a general setting for the analysis of these methods, showing that the methods yield approximate solutions of the same convergence order as the best approximation from the subspace. These augmentation methods allow us to develop fast, accurate and stable nonconventional numerical algorithms for solving operator equations. In particular, for second kind equations, special splitting techniques are proposed to develop such algorithms. These algorithms are then applied to solve the linear systems resulting from matrix compression schemes using wavelet-like functions for solving Fredholm integral equations of the second kind. For this special case, a complete analysis for computational complexity and convergence order is presented. Numerical examples are included to demonstra

关键词： Multilevel augmentation methods operator equations Predholm integral equations of the second kind.

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Iterative Solutions for a Non-monotone Binaryoperator equations and operator System of equations

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Chinese Quarterly Journal of Mathematics 2004年第1期19卷 69-74页

作者： ZHANGFei-ran ZHOUXiao-zhong DepartmentofPrintEngineering theAdvancedCollegeofShanghaiPublishingPrintShanghai200093China DepartmentofMathematics ShangqiuTeacher＇sCollegeShangqiu476000China

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.

关键词： cone and partial ordering operator equations anti-mixed monotone

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Existence and Uniqueness of Solution of Some Increasing operators and Applications

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Chinese Quarterly Journal of Mathematics 2008年第2期23卷 240-244页

作者： HAO Jian-li Department of Mathematics Shangqiu Teacher＇s College Shangqiu 476000 China

By using the cone theory and the monotone succession skills, it is studied the existence uniqueness of fixed point for a class of increasing operators without continuity and compactness and concave or convex conditions in Banach spaces. The results presented here improve and generalize some corresponding results for increasing operator.

关键词： cone and partial ordering increasing operators operator equations

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