基于Brouwer不动点定理的经济均衡问题

根据Vasile I．Istratescu的思路,完善了Brouwer不动点定理的泛函分析证明方法,并运用Brouwer不动点定理证明了纯交易市场下一般经济均衡的存在性．     

Ishikawa迭代收敛点与最佳逼近元

研究了Ishikawa迭代收敛点与平均非扩张映射的不动点集中的最佳逼近元之间的关系.证明了Ishikawa迭代收敛点必是平均非扩张映射的不动点集中的最佳逼近元.     

Mbius变换的不动点与矩阵的特征值

利用Mbius变换的不动点方程和矩阵特征方程的共性,讨论了Mbius变换的不动点与矩阵特征值之间的密切关系,并利用Mbius变换的不动点理论,给出了二阶复矩阵对角化的一种新方法.     

Banach空间中一阶非线性脉冲奇异终值问题的唯一正解

文章利用不动点定理结合迭代技巧,获得Banach空间中一阶非线性脉冲奇异终值问题的唯一正解,给出带有误差估计的正解迭代序列,且文中的条件很容易被验证.     

HOMOTOPY PERTURBATION SOLUTION AND PERIODICITY ANALYSIS OF NONLINEAR VIBRATION OF THIN RECTANGULAR FUNCTIONALLY GRADED PLATES

In this paper nonlinear analysis of a thin rectangular functionally graded piate is formulated in terms of von-Karman＇s dynamic equations. Functionaily Graded Material （FGM） properties vary through the constant thickness of the plate at ambient temperature. By expansion of the solution as a series of mode functions, we reduce the governing equations of motion to a Duffing＇s equation. The homotopy perturbation solution of generated Duffing＇s equation is also obtained and compared with numerical solutions. The sufficient conditions for the existence of periodic oscillatory behavior of the plate are established by using Green＇s function and Schauder＇s fixed point theorem.     

EXISTENCE OF POSITIVE SOLUTIONS TO A THREE-POINT BOUNDARY VALUE PROBLEM FOR SECOND ORDER DYNAMIC EQUATIONS WITH DERIVATIVE ON TIME SCALES

In this paper, we consider the existence of positive solutions to a three-point boundary value problem for second order dynamic equations with derivative on time scales.Applying Leggett-Williams fixed point theorem, we obtain at least three positive solutions to the problem. An example is also presented to illustrate the applications of the results obtained.     

带有p-Laplacian算子的分数阶微分方程多点边值问题正解的存在性

在以下带有p-Laplacian算子的分数阶微分方程多点边值问题中:{D_0~β+(Φ(D_0~α+u(t)))=λf(u(t)),0t1,2α≤3,1β≤2,u(0)=u'(0)=0,u(1)=■β_iu(ξ_i),Φ(D_0~α+u(0))=(Φ(D_0~α+u(1)))'=0,其中D_0~α+,D_0~β+是Riemann-Liouville分数阶导数,f∶[0,+∞)→[0,+∞)是连续函数,文章的新奇之处在于运用Guo-Krasnoselskii不动点定理来研究了一类含参量的带有p-Laplacian多点边值问题正解的存在性及不存在性.     

非自渐近非扩张型映象具误差的Reich-Takahashi粘滞迭代逼近

在具一致Gateaux可微范数的Banach空间中研究非自渐近非扩张型映象具有误差的Reich-Takahashi粘滞迭代序列的收敛性,在没有任何有界条件下,建立了具误差的Reich-Takahashi粘滞迭代序列的强收敛于非自渐近非扩张型映象的不动点定理.     

一类无穷区间上的三阶两点边值问题解的存在性

研究一类无穷区间上的三阶两点边值问题:{x(′″)(t)+a(t)f(t,x(t),x′(t),x″(t))=0,t∈(0,+∞),x(0)=0,x′(0)-bx″(0)=0,x″(+∞)=c,其中a∈C([0,+∞),(0,+∞)),f∈C([0,+∞)×R 3,R),b≥0,c∈R.综合运用上下解方法和Schauder不动点定理,得到了上述三阶无穷边值问题解的存在性.     

无穷区间上含参数分数阶微分方程积分边值问题正解的存在性

考虑一类无穷区间上含参数的Riemann-Liouville型分数阶微分方程积分边值问题.运用锥压缩-锥拉伸不动点定理,建立并证明了该边值问题在无穷区间上正解的存在性与不存在性定理,并给出一个应用实例.