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point theorem
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  点定理
     A COMMON RANDOM FIXED POINT THEOREM FOR A SEQUENCE OF MULTIVALUED MAPPINGS
     多值映象序列的公共随机不动点定理
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     THE APPLICATIONS OF THE FIXED POINT THEOREM TO THE STABILITY THEORY
     不动点定理在稳定性理论中的应用
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     ON A RANDOM FIXED POINT THEOREM FOR MULTIVALUED MAPPINGS
     关于多值映象的一个随机不动点定理
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     The Fixed Point theorem of The Completely Continuous Operator
     全连续算子的不动点定理
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     ON SOME FIXED POINT THEOREM FOR NONLINEAR CONTRACTIVE TYPE MAPPINGS ON A 2-METRIC SPACE
     关于2-距离空间中非线性压缩映象的不动点定理
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  “point theorem”译为未确定词的双语例句
     Where η∈(0,1),0<αη<1,b is a parameter, a:〔0,1〕〔0,∞) and f:〔0, +∞ )〔0,+∞) are continuous. Our approach is based on the Schauder fixed point theorem.
     其中η∈(0,1),0<αη<1,a:〔0,1〕〔0,+∞)连续,f:〔0,+∞)〔0,+∞)连续.
短句来源
     Fuzzy Generalization of The Kakutani-ky Fan Fixed Point Theorem
     Kakutani-Ky Fan不动点定理的Fuzzy推广
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     We are concerned with the periodic BVP on for the Lienard equation x+f(x)x+g(t, x)=e(t)x(0)=x(T), x(0)=x(T)and Laray-Schauder fixed point theorem is used in the studies of the existence of the periodic solutions.
     主要利用Leray-Schauder不动点理论研究Lienard方程周期边值问题x+f(x)x+g(t,x)=e(t)x(0)=x(T),x(0)=x(T)的正解及多个正解的存在性.
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     On Fuzzy Generalization of the Kakutani-ky Fan Fixed Point Theorem
     关于Kakutani-Ky Fan不动点定理的Fuzzy推广
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     Using the exponential dichonomyand fixed point theorem,the existence and stability of periodic solutions for a class of integral differential systems with infinite delayx′(t)=A(t)x(t)+∫t-∞C(t,s)x(s)ds+∫t-∞D(t,s)x′(s)ds+b(t)are discussed. Some effective results are obtained.
     考虑如下周期系统x′(t)=A(t)x(t)+t∫-∞C(t,s)x(s)ds+t∫-∞D(t,s)x′(s)ds+b(t)的周期解存在性与稳定性问题,给出其周期解存在的充分条件.
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  相似匹配句对
     On the Four-point-theorem of Nevanlinna
     关于Nevanlinna四值定理
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     ON THE H.POINCARE FIXED-POINT THEOREM
     关于H.Poincare不动点定理
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     D theorem.
     A. D提出的结论。
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     Theorem.
     定理:设Ω(?)
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  point theorem
We show the following: if there exists a k-variety which is birational to X and which has a smooth k-rational point, then X also has a k-rational point (Theorem 5.7).
      
By means of somea priori estimates of the solution and the Leray-Schauder's fixed point theorem, we prove the existence and the uniqueness theorems of the generalized global solution of the mentioned problem.
      
By the Schauder-Tychonoff fixed-point theorem, we investigate the existence and asymptotic behavior of positive radial solutions of fully nonlinear elliptic equations inRn.
      
This paper proposes a formally stronger set-valued Clarke's fixed point theorem.
      
By this theorem we can improve a fixed point theorem for weakly inward contraction set-valued mapping of D.
      
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In the present paper,we study the boundedness and stability of solutions of the following n-dimensional system of differential equations: dx/dt=A(t)x+f(t,x) x(t_0)=x_0 (1.1) where A(t)is a contiouous n×n matrix for t≥t_0≥0 and f(t,x)is a con- tinuous vector function for t≥t_0,x∈D={x||x|

In the present paper,we study the boundedness and stability of solutions of the following n-dimensional system of differential equations: dx/dt=A(t)x+f(t,x) x(t_0)=x_0 (1.1) where A(t)is a contiouous n×n matrix for t≥t_0≥0 and f(t,x)is a con- tinuous vector function for t≥t_0,x∈D={x||x|0 is a certain constant or+∞.Then the solution of(1.1)passing through(t_0,x_0)can be continued to the interval(t_0,t_0+α)and |x(t)|≤y(t) for t∈[t_0,t_0+α In §3,§4,we use the fundamental theorem to obtain some ratiher general criteria for boundedness and stability of solutions of(1.1)which include a series of results concerned [1] [2] [3] [6],and in this manner one may see the internal relation between these results.In this paper we also come to a similar result obtained by Stokes [16]which relies on a fixed point theorem for locally convex topological linear space due to Tychonoff.

本文討論n维方程组(1.1)。在假設(1.4)与(1.5)之下,得基本定理——若方程(2.7)的最大解要延拓,則方程组(1.1)的解的范不超过它,且也可延拓。由此给出(1.1)的解的有界性和稳定性的判別法,这概括了一系列的有关結果,如文献[1]、[2]、[3]、[6]、[16]、从而看出这些結果的相互关系。

This paper has established fixed point index for condensing maps inordered Banach Spaces and deduced some positive fixed point theorems.

本文对半序Banach空间中锥上的凝聚映射建立了不动点指数,并用其导出了一些正不动点定理,给出了存在正解的条件。

To find the sectionally holomorphic veclor ■(P)≡(φ_0,φ_1,φ~2,φ~3):1) Which is holomorphic in D~+ and D~-, i.e. satisfying the system of partial differential equations of elliptic-type of the first order in spaceand satisfying on the boundary surface ∑ the boundary condition(H)_l ■~+(P_0)=G(p_0)■~-(p_0)+■(P_0)Where G(p_0)=[G_(ij)(p_0)],ij=1,2,3,4, which is a given nonsingular function matrix on ∑ and (?)(P_0)=(g_1,g_2,g_3,g_4) is a given function vector and they are satisfying the H (Hlder) condition on ∑. By...

To find the sectionally holomorphic veclor ■(P)≡(φ_0,φ_1,φ~2,φ~3):1) Which is holomorphic in D~+ and D~-, i.e. satisfying the system of partial differential equations of elliptic-type of the first order in spaceand satisfying on the boundary surface ∑ the boundary condition(H)_l ■~+(P_0)=G(p_0)■~-(p_0)+■(P_0)Where G(p_0)=[G_(ij)(p_0)],ij=1,2,3,4, which is a given nonsingular function matrix on ∑ and (?)(P_0)=(g_1,g_2,g_3,g_4) is a given function vector and they are satisfying the H (Hlder) condition on ∑. By using the double integral of Cauchy typeWhere be 4×4 matrices, they are transpose of each other.γ_(PQ)=γ(P,Q)=((x-ξ)~2+(y-η)~2+(z-ζ)~2)~(1/2) be the distance of two points p(ξ,η,ζ,) and Q(x,y,z).By ■(α,β,γ) denote the outer normal of D~+ on the surface ∑ at the poinr Q. The matrix M(P,Q) is Called a Cauchy kernel matrix, the point P=Q is an isolated singular point of second order of M(P,Q).Reducing the Hilbert boundary problem in space (H)_l to the System of singulra integral equations with Cauchy kernel matrix;WhereUsing the Banach fixed point theorem to prove the existence and uniqueness theorem for the system of singuler integral equations (I)_l, then the above Hilbert boundary value problem in space (H)_l has a unique solutiou under some conditions.By means of the Schauder fixed-point theorem, which enables us to prove existence theorem for nonliean Hilbert boundary value problem in space:(H)_n G■~+(P_0)+K■~-(P_0)+λ■(P_0,■~+(P_0),■~-(P_0))=0Where G(P_0)=[G_(ij)(P_0)]i,j=1,2,3,4; K(P_0)=[K_(ij)(P_0)]i,j=1,2,3,4, which are the given nonsingular function matrices on ∑, and det|G±K|≠0, λ≠0 is a parameter, ■≡■(f_1,f_2,f_3,f_4) is a given non-linear Continuous function vector of ■~+(P_0) and■~-(P_0) and satisfying H(Hlder) condition on ∑.Supposing that also satisfies some supplementary conditions, it is shown that the non-linear Hilbert boundary value problem in space (H)_n has a uniquc solution also.

本文是研究空间的线性与非线性的Hilbert边值问题,该问题是提出的,但他只解决了常系数的情形。作者首先证得了H((?),Σ)是Banach空间,再用Banach不动点定理证得变系数的空间线性Hilbert边值问题解的存在性与唯一性。同时用Schauder不动点原理证得空间非线性Hilbert边值问题解也是存在的,然后加上适当条件便可证得解亦呈唯一的。

 
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