分数阶微分方程多点分数阶边值问题

研究分数阶微分方程多点分数阶边值问题解的存在性与唯一性,利用不动点定理,得到了边值问题存在唯一解和至少存在1个解的充分条件.     

目标属性为真假值函数的多目标决策问题解的存在性与求解方法

本文建立了一类目标属性为真假值函数的多目标决策模型，定义了相应有效解、弱有效解与最优解．并在此基础上，对有效解与弱有效解的存在性、求解等问题进行了探讨．     

线性规划无穷多最优解的讨论

利用线性规划单纯形表对线性规划原问题存在无穷多最优解和对偶问题存在无穷多最优解的情况进行了讨论,并分析了对偶问题存在无穷多最优解情况下的影子价格的方向性。最后以实例说明了各种情况。对初学者加深理解及决策者决策参考有一定帮助     

一阶多参数模糊微分方程及定解问题

在单参数模糊微分方程基础上研究了一阶多参数模糊微分方程和模糊初值问题,利用刻画方程的解与刻画参数的关系给出了多参数模糊微分方程解存在的条件,最后给出了具体算例.表明,多参数模糊微分方程具有广泛的工程应用背景.     

一类具有多偏差变元的Liénard系统的反周期解

研究了一类具有多偏差变元的Liénard系统的反周期解,获得了该系统反周期解的存在性与全局指数稳定性的新充分条件.     

关于P4P问题解数的一些研究

本文研究了计算机视觉中P4P问题的多解问题,运用几何方法,分析了P4P问题的多解现象,获得了P4P问题存在5个解的必要条件.     

绝对值方程算例分析

分别给出了绝对值方程存在唯一解的算例、存在2~n个解的算例、存在无穷多个解的算例以及无解的算例,并分析了这些算例中矩阵奇异值的特点.     

二维空间中广义Davey-Stewartson系统整体解存在的最佳条件

根据基态的特征 ,首先在二维空间中导出了广义Davey Stewartson系统解爆破和整体存在的最佳条件 ;其次得到了整体解存在的一个最佳充分条件 ;最后证明了当初值为多小时 ,该系统的整体解存在 .     

一类微分方程组的多重正解

本文讨论了 Ｂａｎａｃｈ空间中 Ｓｔｕｒｍ－Ｌｉｏｕｖｉｌｌｅ问题正解的存在性与多解性，通过线性算子的谱半径，给出其正解存在与多解的条件．     

一类具多偏差变元的高阶中立型微分方程周期解的存在唯一性

利用重合度理论,研究了一类具多偏差变元高阶中立型泛函微分方程的周期解,获得这类方程至少存在和至多存在一个T-周期解的充分性条件,其中周期解的先验界估计与方程的滞量有关.文中的主要结果改进和推广了相关文献的主要定理.     

Multiple solutions for a class of biharmonic elliptic systems with Sobolev critical exponent

In this paper, we study the existence and multiplicity of nontrivial solutions for a class of biharmonic elliptic systems with Sobolev critical exponent in a bounded domain. By using the variational method and the Nehari manifold, we obtain the existence and multiplicity results of nontrivial solutions for the systems.     

Multiplicity of solutions for resonant elliptic systems

We establish the existence and multiplicity of solutions for some resonant elliptic systems. The results are proved by applying minimax arguments and Morse theory.     

Existence and multiplicity of nontrivial solutions for quasilinear elliptic systems

The existence and multiplicity of nontrivial solutions are obtained for the quasilinear elliptic systems by the linking argument, the cohomological index theory and the pseudo-index theory.     

Existence and multiplicity results for critical growth polyharmonic elliptic systems

In the present paper, we deal with the existence and multiplicity of nontrivial solutions for a class of polyharmonic elliptic systems with Sobolev critical exponent in a bounded domain. Some new existence and multiplicity results are obtained. Our proofs are based on the Nehari manifold and Ljusternik–Schnirelmann theory. Copyright © 2013 John Wiley & Sons, Ltd.     

MULTIPLE SYMMETRIC RESULTS FOR A CLASS OF BIHARMONIC ELLIPTIC SYSTEMS WITH CRITICAL HOMOGENEOUS NONLINEARITY IN R~N

This paper is dedicated to studying the existence and multiplicity of symmetric solutions for a class of biharmonic elliptic systems with critical homogeneous nonlinearity in RN. By virtue of variational methods and the symmetric criticality principle of Palais,we establish several existence and multiplicity results of G-symmetric solutions under certain appropriate hypotheses on the parameters and the weighted functions.     

Existence and multiplicity results for partially superquadratic elliptic systems

In this paper we establish the existence and multiplicity of solutions for a class of partially superquadratic elliptic systems by using the Morse theory.     

Positive solutions for some nonlocal and nonvariational elliptic systems

Using fixed point techniques, we study the existence and multiplicity of positive radial solutions for two classes of nonlocal elliptic systems defined on bounded annular domains or exterior domains. To this end, we reduce our problem to second-order functional ordinary elliptic systems. Our approach also allows us to study systems involving various orders, which serve as models for the suspension bridge equations.     

Multiple symmetric results for singular quasilinear elliptic systems with critical homogeneous nonlinearity

This paper deals with the existence and multiplicity of symmetric solutions for a class of singular quasilinear elliptic systems with critical homogeneous nonlinearity in a bounded symmetric domain. Applying variational methods and the symmetric criticality principle of Palais, we establish several existence and multiplicity results of G‐symmetric solutions under some appropriate assumptions on the weighted functions and the parameters. Copyright © 2016 John Wiley & Sons, Ltd.     

椭圆边值系统的正径向解的存在性与多解性

通过利用锥拉伸及锥压缩型的Krasnosel‘skii不动点定理，我们研究了一类椭圆边值系统的正径向解的存在性，非存在性与多解性。     

环域上一类二阶非线性椭圆系统的正对径解

研究环域上一类非线性二阶椭圆系统的正对径解的存在性和多解性，章的主要思想是锥拉伸与锥压缩型的Krasnosel’skii不动点定理的局部应用。