nonlinear functional analysis meaning in English
非线性泛函分析
Examples
- The study for the general principle on ordered sets in nonlinear functional analysis
非线性泛函分析序集一般原理的研究 - This paper mainly further studies several focus problems in nonlinear functional analysis , unites and generalizes some known results in recent literature
本文主要对非线性泛函分析中的几个热点问题作了进一步的分析和研究，对已有的结果进行了统一和推广。 - Professor guo dajun has summarized in his work [ 7 ] . such several important tasks and theirs application of nonlinear functional analysis as typical nonlinear operators , hammerstein integral operations , ordinarily and partially differential equations . the cone theory , the positive solutions of nonlinear operator equations , the number and the branch of solutions , and so on . reference [ 1 ] includes all levels of results of the domain such as nonlinear functional analysis
郭大钧先生在专著[ 7 ]中对非线性泛函分析的几个重要课题及其应用，诸如典型的非线性算子、 hammerstein积分方程、常、偏微分方程、迁移方程、锥理论及非线性算子方程的正解、非线性算子拓扑度和不动点定理以及固有值、解的个数与分支，都做了系统的概括和总结 - Throughout the following of this section , e denotes a real banach space and p is a cone in e . in chapter , a new three - solution theorem is obtained . moreover , the famous amann ' s and leggett - williams " three - solution theorems in nonlinear functional analysis can be seen as its special cases , namely they are united . so they are improved . the main results can be stated as the following : let d be a nonempty bounded close convex subset in e , and nonnegative continuous functional on d . and is concave while is convex . suppose 0 < d and denote
首先我们约定，在下文中， e是实banach空间， p是e中的锥。在第一章中，我们利用锥理论与不动点指数理论统一了著名的amann三解定理与leggett - williams三解定理。主要结论是：设d是e中的非空有界闭凸集， ，是d上的非负连续泛函，且是凹泛函，是凸泛函。 - Nonlinear functional analysis is a subject . old but fashionable . its abundant theories and advanced methods are providing powerful and fruitful tools in solving ever increasing nonlinear problems in the fields of science and technology . though the theories of integral and differential equations in banach spaces , as new branches of nonlinear functional analysis . have developed for no more than thirty years , they are finding extensive applications in such domains as the critical point theory , the theory of partial differential equa - tions , eigenvalue problems . and so on , are attracting much more attentions from both pure and applied mathematicians
非线性泛函分析是一门既悠久又现代的学科，它的丰富理论和先进方法为解决当今科技领域层出不穷的非线性问题提供了卓有成效的工具，作为自非线性泛函分析中衍生发展起来的新的分支， banach空间微分方程和积分方程理论虽经历了不足三十年的发展过程，然而它已被广泛应用于诸如临界点理论，偏微分方程理论，特征值问题等许多领域，其重要性日益凸现出来