不动

Firstly, by constructing the Lyapunov function with a special structure, a prior estimate is obtained. Secondly, with the help of Green\'s function, the original problem is transformed into an equivalent operator equation, and the fixed point theory of contraction mapping in a Banach space guarantees the existence and uniqueness of the global solution.

首先，构造具有特殊结构的Lyapunov函数，得到解的先验估计；其次，借助Green函数将原方程等价变换成算子方程，Banach压缩映射的不动点定理保证了全局解的存在唯一性；最后通过常微分方程的定解，证明了主要结论，即平凡解全局渐近稳定。

As for the existence of positive solutions, the cone theory and the fixed point index of condensing mapping are employed, and the results of the existence of positive solutions are obtained in the case of superlinear and sublinear. The conclusions extend and improve the existence theorem which Lou Ben-dong extablished in 1996 about the question of Sturm-Liouville of Banach spaces.

三、对于正解存在性问题，我们应用凝聚映射的不动点指数理论，分别在超线性与次线性情形下进行讨论，获得了一些正解存在的结果，主要结果推广和改进了1996年Lou Ben-dong对Banach空间Sturm-Liouville问题所建立的存在性定理。

We also proved the space made of mapping of Caristi fixed point theorem is complete .

另外还证明了Caristi不动点定理中对应映射组成的空间是完备的。

Local existence is proved by using a fixed point theorem.

本文利用不动点定理证明了局部解的存在性。

Since they are based on Banach fixed point theorem to construct the local solution.

这两种方法都是用Banach不动点定理构造局部解。

In chapter one, by using Krasnoselskii s fixed point theorem, necessary and sufficient c...

第一章讨论了一类带阻尼项的高阶非线性中立型差分方程正解的存在性，利用Krasnoselskii不动点定理，得到了非振动解存在的若干充分必要条件，这些结果改进和推广了一些已知的结果。

The existence and uniqueness of the solutions are proved by Leray-Schauder fixed point theorem.

相应解的存在唯一性由Leray-Schauder不动点定理得以证明。

Under the suitable conditions, the existence of positive solutions is established by using the abstract fixed point theorem.

研究几类二阶非线性常微分方程组的边值问题，在合适的条件下，利用锥拉伸不动点定理获得了其正解的存在性。

The third section is the main part of this paper, where we discuss the existence of positive entire solutions by the super-subsolution method and some fixed point theorem.

第三章是本文的主要部分，主要用上下解方法和不动点定理解决解的存在性问题，推广了已有的成果。

We prove that the existence and uniqueness of solution of the system of generalized nonlinear variational inclusions by using the fixed point theorem.

运用不动点定理，我们证明了广义非线性变分包含组解的存在性与唯一性。

Singer Leona Lewis and former Led Zeppelin guitarist Jimmy Page emerged as the bus transformed into a grass-covered carnival float, and the pair combined for a rendition of "Whole Lotta Love".

歌手leona刘易斯和前率领的飞艇的吉他手吉米页出现巴士转化为基层所涵盖的嘉年华花车，和一双合并为一移交&整个lotta爱&。

This is Kate, and that's Erin.

这是凯特，那个是爱朗。