非线性滞后型微分方程非局部边值问题的正解

By using Krasnoselskii‘s fixed-point theorem on a suitable cone, several existence results and corresponding properties of positive solutions of nonlocal boundary value problem for nonlinear retarded differential equation are obtained.     

Smooth Solution to the 1-Dimensional Spin Equations of Antiferromagnets

In this paper, the global existence and uniqueness of a smooth solution to the periodic initial-value problem of the spin equations of antiferromagnets in 1 dimension are proved.     

Stampacchia Generalized Vector Quasiequilibrium Problems and Vector Saddle Points

In this paper, Stampacchia generalized vector quasiequilibrium problem and generalized vector loose saddle points for set-valued mappings are introduced. By using the scalarization method and the fixed-point theorem, existence theorems are established.This work was supported by the National Natural Science Foundation of China and the Natural Science Foundation of Jiangxi Province, China. The author is grateful to Professor F. Giannessi and the referee for valuable comments and careful reading improving the original draft.Communicated by F. Giannessi     

Symmetric strong vector quasi-equilibrium problems

In this paper, we introduce the symmetric strong vector quasi-equilibrium problem. We then demonstrate that the symmetric strong vector quasi-equilibrium problem is solvable under the suitable assumptions. As an application, we get an existence theorem of the strong saddle points of vector-valued functions. In addition, we give a characterization of vector-valued properly quasi-convex functions. This work was supported by the Natural Science Foundation of China and the Natural Science Foundation of Jiangxi Province, China     

The existence of positive solution for singular boundary value problems of first order differential equation on unbounded domains

By constructing a special cone and using cone compression and expansion fixed point theorem, this paper presents some existence results of positive solutions of singular boundary value problem on unbounded domains for a class of first order differential equation. As applications of the main results, two examples are given at the end of this paper. Supported by the National Natural Science Foundation of China (No. 10671167) and the Natural Science Foundation of Liaocheng University (31805).     

一个耦合系统自由边界问题的整体古典解

§ 1　ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｔｈｉｓｐａｐｅｒｗｅｄｉｓｃｕｓｓｔｈｅｇｌｏｂａｌｃｌａｓｓｉｃａｌｓｏｌｕｔｉｏｎｏｆａｍｕｌｔｉｄｉｍｅｎｓｉｏｎａｌｑｕａｓｉｓｔａｔｉｏｎａｒｙｐｒｏｂｌｅｍ .Ｔｈｅｐｒｏｂｌｅｍｃｏｍｅｓｆｒｏｍｔｈｅｄｉｓｃｕｓｓｉｏｎｏｆａｇｒｏｗｔｈｍｏｄｅｌｏｆｓｅｌｆｍａｉｎｔａｉｎｉｎｇｐｒｏｔｏｃｅｌｌ(ｓｅｅ [1— 3])ｉｎｍｕｌｔｉｄｉｍｅｎｓｉｏｎａｌｃａｓｅ .Ｔｈｅｐｒｏｔｏｃｅｌｌｃａｎｂｅｖｉｓｕａｌｉｚｅｄａｓｈａｖｉｎｇａｐｏｒｏｕｓｓｔ…     

Finite difference method of first boundary problem for quasilinear parabolic systems (V)

Iterative difference schemes for the first boundary problem of the quasilinear parabolic system are established and the convergence of the difference solution for the iterative difference schemes to the unique solution of the problem is proved. Project supported by the National Natural Science Foundation of China and the Foundation of CAEP.     

Different Conjugate Dual Problems in Vector Optimization and Their Relations

In this paper, three kinds of conjugate dual problems are constructed by virtue of different perturbations to a constrained vector optimization problem. Weak duality, strong duality, and some inclusion relations for the image sets of the three dual problems are established. This research was partially supported by the National Natural Science Foundation of China (Grant Number 60574073) and the Natural Science Foundation Project of CQ CSTC (Grant Number 2007BB6117). The authors thank two anonymous referees for valuable comments and suggestions, which helped improving the paper.     

Levitin–Polyak well-posedness of vector equilibrium problems

In this paper, two types of Levitin–Polyak well-posedness of vector equilibrium problems with variable domination structures are investigated. Criteria and characterizations for two types of Levitin–Polyak well-posedness of vector equilibrium problems are shown. Moreover, by virtue of a gap function for vector equilibrium problems, the equivalent relations between the Levitin–Polyak well-posedness for an optimization problem and the Levitin–Polyak well-posedness for a vector equilibrium problem are obtained. This research was partially supported by the National Natural Science Foundation of China (Grant number: 60574073) and Natural Science Foundation Project of CQ CSTC (Grant number: 2007BB6117).     

Center and isochronous center problems for quasi analytic systems

This paper considers the problems of determining center or focus and isochronous centers for the planar quasi-analytic systems. Two recursive formulas to determine the focal values and period constants are given. The convergence of first integral near the center is proved. Using the general results to quasi-quadratic systems, the problem of the isochronous center of the origin is completely solved. This research is partially supported by the National Natural Science Foundation of China (10671179 and 10771196) and the Natural Science Foundation of Yunnan Province (2005A0092M)     

Global Entropy Solutions of the Cauchy Problem for Nonhomogeneous Relativistic Euler System

We analyze the 2×2 nonhomogeneous relativistic Euler equations for perfect fluids in special relativity. We impose appropriate conditions on the lower order source terms and establish the existence of global entropy solutions of the Cauchy problem under these conditions.     

Existence,orbital stability and instability of solitary waves for coupled BBM equations

This paper is concerned with the orbital stability/instability of solitary waves for coupled BBM equations which have Hamiltonian form. The explicit solitary wave solutions will be worked out first. Then by detailed spectral analysis and decaying estimates of solutions for the initial value problem, we obtain the orbital stability/instability of solitary waves.     

Connectedness of the Solution Sets and Scalarization for Vector Equilibrium Problems

In this paper, we introduce the concepts of globally efficient solution and cone-Benson efficient solution for a vector equilibrium problem; we give some scalarization results for Henig efficient solution sets, globally efficient solution sets, weak efficient solution sets, and cone-Benson efficient solution sets in locally convex spaces. Using the scalarization results, we show the connectedness and path connectedness of weak efficient solution sets and various proper efficient solution sets of vector equilibrium problem. This research was partially supported by the National Natural Science Foundation of China and the Natural Science Foundation of Jinxing Province, China.     

<Emphasis Type="Italic">m</Emphasis> Components-admissible solutions of systems of higher-order partial differential equations on <Emphasis Type="Italic">C</Emphasis><Superscript><Emphasis Type="Italic">n</Emphasis></Superscript>

Using value distribution theory and techniques in several complex variables,we investigate the problem of existence of m components-admissible solutions of a class of systems of higher-order partial differential equations in several complex variables and estimate the number of admissible components of solutions.Some related results will also be obtained.     

Non-constant stationary solutions to a prey-predator model with diffusion

In this paper, a nonlinear predator reproduction and prey competition model with diffusion is discussed. Some existence and non-existence results concerning non-constant positive steady-states are presented using topological degree argument and the energy method, respectively. The first author was supported by the National Natural Science Foundation of China (No. 10771032) and the Natural Science Foundation of Jiangsu province BK2006088, and the second author was supported by National Natural Science Foundation of China (No. 10601011).     

EQUIFOCAL HYPERSURFACES IN SYMMETRIC SPACES

This note investigates the multiplicity problem of principal curvatures of equifocal hypersurfaces in simply connected rank 1 symmetric spaces. Using Clifford representation theory, and the author also constructs infinitely many equifocal hypersurfaces in the symmetric spaces. Project supported by the National Natural Science Foundation of China (No. 19925104), RFDP and the Qiu-Shi Science and Technology Foundation.     

Sharp threshold of global existence for the Klein-Gordon equations with critical nonlinearity

In this paper, we present a cross-constrained variational method to study the Cauchy problem of the nonlinear Klein-Gordon equations with critical nonlinearity in two space dimensions. By constructing a type of cross-constrained variational problem and establishing so-called cross-invariant manifolds of the evolution flow, we establish a sharp threshold of global existence and blowup of it. Furthermore, we answer the question： How small are the initial data if the solution exists globally.     

Idempotent completions of operator partial matrices

Necessary and sufficient conditions are obtained for operator partial 2 × 2 matrices to have an idempotent completion, and all such completions are parametrically represented. Project supported by National Natural Science Foundation of China and Provincial Natural Science Foundation of Shanxi     

A level set method to reconstruct the discontinuity of the conductivity in EIT

In this paper, one level set method is applied to finding the interface of discontinuity of the conductivity in EIT(electrical impedance tomography) problem. By choosing one suitable velocity function, a level set reconstruction algorithm is proposed. The theoretical results for EIT problem and regularization are given. Finally the numerical examples demonstrate that the reconstruction algorithm is efficient and stable. The work was supported by the National Natural Science Foundation of China (Grant Nos. 10431030, 10771138), the Shanghai Natural Science Foundation (Grant No. 07JC14001), the National Basic Research Program (Grant No. 2005CB321701) and Ministry of Education of China and State Administration of Foreign Experts Affairs of China under an 111 project (Grant No. B08018).     

On Eigenvalue Intervals and Eigenfunctions of Nonresonance Singular Dirichlet Boundary Value Problems

In this paper we shall consider the nonresonance Dirichlet boundary value problemwhere λ>0 is a parameter, p>0 is a constant. Intervals of A are determined to ensure the existence of a nonnegative solution of the boundary value problem. For λ=1, we shall also offer criteria for the existence of eigenfunctions. The main results include and improve on those of [2,4,6,8].