不动点定理

The existence of periodic solutions to the second order ordinary differential equation in Banach space is discussed.

本文利用半序理论，非紧性测度，凝聚映射的拓扑度，不动点定理及锥上不动点指数理论，讨论了Banach空间E中二阶常微分方程周期边值问题解的存在性，主要结果有一。

This paper considered the existence of solutions to boundary value problem of several kinds of nonlinear sys...

本文利用锥理论，不动点理论，Krasnoselskii不动点定理等研究了两类奇异微分方程非线性边值问题解的情况，得到了一些新成果。

Thus there has been an increased interest in studying theexistence and multiplicity of periodic boundary value problem.

因而受到人们广泛的关注，发展和解决这类问题的一些有效的方法如Lyapunov泛函方法，不动点和范数形式的锥拉伸锥压缩不动点定理等。

By using generalized-weak commutativity mapping, the existence of common fixed point for this class of contractive type mappings is studied in complete metric space, a common fixed point theorem for contractive type mappings is obtained, which largely improve and extend the corresponding results in some references.

通过使用映象的广义弱交换条件，在完备度量空间中研究了更为广泛的一类压缩型映象的公共不动点的存在性，给出了一个新的公共不动点定理，从而在很大程度上改进和推广了现有文献中的一些结果。

This paper proves that every probabilistic contraction map from E to E has a unique fixed point, where E is a complete and uniformly local semi-convex probabilistic normed spacer and obtains a fixed point theorem in metric linear spaces.

摘要证明了完备的一致局部半凸概率赋范空间上的概率压缩映象必有唯一不动点，得到了一类度量线性空间中关于伪范数族一致压缩映象的不动点定理。

At first, the existence of extended form of approach to continuous selection for any set valued mapping without any continuity restriction in para-compact metric space is proved ;by the topologically separated mappings , the approximate selection theorem of sub-lower-semi-continuous mapping is established, furthermore , continuous selection problem in H-space is studied. Next, with W-correspondence, an improved variational inequality is obtained ; by the H-KKM mapping ,Ky Fan\'s minimax inequality is generalized to H-space . At last, with H-convexity instead of the linear topological structure, a new version of Browder fixed point theorem is established.Chapter 3 deals with set-valued mapping vector variational inequality and minimax problems.

第二章首先在仿紧的度量空间上对任意的集值映射建立了新的逼近连续选择定理，利用映射的拓扑可分性，在H-空间上建立了次下半连续映射的逼近连续选择定理和一个新的连续选择定理；然后利用W-对应，在H-空间上建立了广义的变分不等式；利用H-KKM映射，在H-空间上建立了广义的KyFan极小极大不等式；最后，利用H-凸性代替拓扑线性结构，在H-空间上建立了一个新型的Browder不动点定理。

By using the cone and partial ordering theory, it is studied that fixed point theorems non-monotone in Banach spaces, some new coupled fixed point theorems are abtained.

利用锥与半序理论，研究Banach空间不具有单调性的一类二元算子的不动点，得出了新的耦合不动点定理，是某些已有结果的改进和推广。

By applying a Fan-Glicksberg type fixed point theorem for upper semicontinuous set-valued mappings with closed acyclic values and a maximum theorem,several existence theorems of weighted Nath-equilibria and Pareto equilibria for the constrained multiobjective games are proved in noncompact locally convex H-spaces.

应用局部凸H－空间内具有闭零调值的上半连续集值映象的Fan－Glicksberg型不动点定理和极大化定理，对无限最优化总理2和约束对策问题在没有线性结构的局部凸H－空间内证明了解的某些新的存在定理，这些定理改进和推广了最近文献中的许多重要结果。

In this paper, by Zorn lemma and cone theory, the existence of the random fixed points for discontinuous increasing operators was discussed and the existence theorems of random fixed point were obtained.

本文利用Zorn引理和锥理论，研究了不连续随机算子的随机不动点的存在性问题，得到了几个有关不连续随机增算子的随机不动点定理。

In the study of the first problem, by using the fixed-point index theorems, we get the existence of boundary value problem in neither superlinear nor sublinear condition.

在第二种形式边值问题的研究中，主要利用Krasnoselskii不动点定理，得到了一些正解存在性定理及正解不存在性定理。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。