查询词典 fixed point theorem

In Chapter 1, we use the upper and lower solutions method, the bootstrap technique and the Schauder fixed point theorem to investigate the existence of periodic solutions and the asymptotic behavior of general time-dependent solutions for periodic reaction-diffusion systems of the following three types:(1) Quasimonotone nondecreasing system;(2) Mixed quasimonotone system;(3) A nonquasimonotone 2-system. The boundary conditions are assumed to be either the Dirichlet condition or linear Robin conditions.

在第一章，我们应用上、下解方法，bootstrap技巧和Schauder不动点定理考察如下三类周期反应扩散方程组的周期稳态解的存在性和一般的时变解的渐近性态：（1）拟单增系统；（2）混拟单调系统；（3）一个非拟单调2-系统，其边界条件是Dirichlet条件或线性Robin条件。

With the method of upper and lower solutions,its associated monotone iterations and the fixed point theorem,the coexistence solutions to a strongly coupled elliptic system are studied.

采用上下解及相应的单调迭代序列的方法，结合Schauder不动点定理，研究带Dirichlet边界条件的两种群的互惠模型强耦合问题共存解。

Although classical Ekeland is equivalent to classical Caristi fixed point theorem, we can not make the same degree of generalization for them.

另外，我们指出即使古典的Caristi不动点定理和Ekeland变分原理是等价的，但是Ekeland变分原理不能和Caristi不动点定理作相同程度的推广。

By using of the decomposition of equation and the Leray-Schauder fixed point theorem, four existence theorems are established.

通过使用方程的分解技巧和Leray-Schauder不动点定理建立了4个存在定理。

Then we prove the existence of positive solutions for difference equations by using fixed point theorem of cone expansion and compression.

另外，对非线性项具有混合单调性的情况，利用不动点指数性质及锥压缩与拉伸不动点定理等方法，得到了差分方程一个正解的存在性。

In the second part, we make use of fixed point theorem of conic expansion and compression to prove the existence of two positive solutions in Banach spaces for ...

第二部分利用锥拉伸与压缩不动点定理证明了Banach空间中非线性项系数带变号的二阶四点边值问题两个正解的存在性。

In the second chapter, we will exploit the skill of the fixed point theorem of cone expansion and compression to study a class of fourth ordered singular differential equation: where /...

有关奇异微分方程边值问题正解的存在性、唯一性、多解性以及正解存在的充分必要条件近年些来获得了广泛的研究。

By constructing a special cone and using cone compression and expansion fixed point theorem, we get the existence of positive solutions.

第二章在抽象空间E中仍然考虑第一章中的2n阶Lidstone奇异边值问题的解的存在性，其中f∈C[(0，1)×P，P]，且在t=0，1处具有奇异性。

The existence and uniqueness of the solution with the help of the Banach fixed point theorem and the theory of operator semigroups are verified .The global exponential stability of KS equation and the global exponential stability and asymptotical stability of macro KS equation with the given boundary feedbacks are proved .

通过Banach不动点原理和算子半群理论证明了方程解的存在性和唯一性，并证明了KS方程在给定的边界反馈条件下是全局指数稳定的及广义的KS方程在给定的边界反馈条件下是全局指数稳定和渐近稳定的。

In this paper, the almost periodic solution for a class of two-degree-of-freedom nonlinear oscillating systems is studied by using the Leray-Schauder fixed point theorem and the method of Liapunov function.

运用Leray-Schauder不动点定理和Liapunov函数方法，研究了一类两自由度非线性振动系统的概周期解，得到了该振动系统概周期解存在的充分条件。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。