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压缩映射原理     
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  contraction mapping principle
     In this paper,with the theory of trigonometrical series and contraction mapping principle,some sufficient conditions for the existence and uniqueness of periodic solution to Duffing equation ax″+bx+g(x(t~τ))=p(t) are obtained.
     利用三角级数理论及压缩映射原理研究了时滞Duffing型方程ax″(t)+bx(t)+g(x(t-τ))=p(t),给出了此类Duffing型方程存在唯一周期解的几个充分条件.
短句来源
     Theorem 2.1 and 2.3 in the paper are the two research findings while Theorem 2.2 has developed Banach′s contraction mapping principle.
     定理2.1和定理2.3是这方面研究的两个结果,定理2.2拓展了Banach压缩映射原理.
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     Second order nonlinear neutral difference equation Δ(a(n)Δ(x(n)+p(n)x(n-τ))+f(n,x(σ(n)))=0is discussed.Using Banach contraction mapping principle,the existence theorems for throughout positive solutions with some limit behavior of this equation is obtained.
     研究了二阶非线性中立型差分方程Δ(a(n)Δ(x(n)+p(n)x(n-τ)))+f(n,x(σ(n)))=0的非振动性. 利用Banach压缩映射原理,得到了这个方程具有某种极限性质的始终正解的存在性定理.
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     he solution of Fredholm instigral equation is deduced by using Banach contraction mapping principle.
     用巴拿赫压缩映射原理导出Fredholm方程的解。
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     Contraction Mapping Principle in Fuzzy Normed Liner Space
     Fuzzy赋范线性空间上的压缩映射原理
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  principle of compressed mapping
     Principle of compressed mapping and its application in finding limit of sequence of numbers
     压缩映射原理在求数列极限中的应用
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     In this paper, the stability and periodic solution of shunting inhibitory cellular neural networks and olfactory cortex neural networks are studied, a set of sufficient criteria are given by applying the theory of Brouwer degree and the principle of compressed mapping and contributing Lyapunov function.
     本文研究了并联限制细胞神经网络和嗅觉皮层神经网络的稳定性及周期解,利用Brouwer度理论、压缩映射原理和构造Lyapunov泛函给出了一系列充分准则。
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  the contraction mapping principle
     Then using the contraction mapping principle and the extension theorem of the solution we prove the existence and uniqueness of the global generalized solutions and the existence and uniqness of the global classical solution.
     。 (9)Cauchq问题.先是通过一个二阶偏微分方程的基本解,把IMBq型方程组归),p)的初值问题转化为等价的积分方程组,然后利用压缩映射原理、解的延拓定理等证明了归),问的初值问题的整体广义解和整体古典解的存在唯一性.
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     By using the exponential dichotomy, its roughness theory and the contraction mapping principle, under some suitable conditions some sufficient conditions for the existence and uniqueness of almost periodic solutions and bounded solutions of these systems are obtained.
     (dx)/(dt)=A(t,∈)x+f(t,x,μ)+∈g(t,x,∈), (3)利用压缩映射原理和指数二分性及其粗糙度理论,在适当的条件下,得到了上述系统的概周期解和有界解的存在性和唯一性的一些充分条件。
短句来源
     In this paper, the existence and uniqueness of the local generalized solution of the initial boundary value problem for a nonlinear hyperbolic equation are proved by the contraction mapping principle and the sufficient conditions of blow_up of the solution in finite time are given.
     本文应用压缩映射原理证明一非线性双曲型方程的初边值问题存在唯一局部广义解 ,并给出此问题的广义解爆破的充分条件
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     Associated with the variational systems of non-perturbation systems, a kind of almost periodic perturbation system with deviating argument is investigated by using the contraction mapping principle. A set of sufficient conditions for the existence and uniqueness of the systems is obtained.
     结合非扰动系统关于其概周期解的变分方程系,运用压缩映射原理研究一类具有偏差变元概周期扰动系统的概周期解,获得系统存在唯一概周期解的一组充分条件.
短句来源
  contraction mapping theorem
     Based on contraction mapping theorem of analysis mathematics, the non-steady flow mathematical model of mine ventilation network was analyzed. The convergent condition of numerical solution to the mathematical model was obtained, and the selection scheme of circuit according to inertial coefficient searching the least spanning tree was put forward. Theoretical basis on the numerical solution convergence of the non-steady flow mathematical model is provided.
     利用分析数学的压缩映射原理,对矿井通风网络非稳定流动数学模型进行了分析,得出了数学模型数值解收敛的条件,确定了以惯性系数排序选择最小生成树的回路选择方案,为矿井通风网络非稳定流动数学模型数值解的收敛性提供了理论依据.
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  contraction mapping principle
The solvability of these equations is studied by the contraction mapping principle.
      
After a number of estimates, we utilize the Contraction Mapping Principle to prove the global well-posedness of this equation in a certain discrete Banach space.
      
We present a numerical algorithm which is based on successive iterations to obtain a fixed point guaranteed by the Contraction Mapping Principle.
      
Generalized contraction mapping principle in intuitionistic Menger spaces and application to differential equations
      
Time local well-posedness for the Maxwell-Schr?dinger equation in the Coulomb gauge is studied in Sobolev spaces by the contraction mapping principle.
      
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  the contraction mapping principle
The solvability of these equations is studied by the contraction mapping principle.
      
After a number of estimates, we utilize the Contraction Mapping Principle to prove the global well-posedness of this equation in a certain discrete Banach space.
      
We present a numerical algorithm which is based on successive iterations to obtain a fixed point guaranteed by the Contraction Mapping Principle.
      
Time local well-posedness for the Maxwell-Schr?dinger equation in the Coulomb gauge is studied in Sobolev spaces by the contraction mapping principle.
      
Then this result as well as the contraction mapping principle is applied to prove the existence theorem for the nonlinear equation.
      
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