In nite Dimensional Morse Theory and Multiple Solution Problems
In nite Dimensional Morse Theory and Multiple Solution Problems
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DOI：
10.1007/978-1-4612-0385-8
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发表时间：
1992
期刊：
影响因子：
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通讯作者：
Kuang-Chao Chang
中科院分区：
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作者：
Kuang-Chao Chang
这本书是基于我1985年在蒙特利尔的课堂讲稿《无限维莫尔斯理论及其应用》，以及1987年在威斯康星大学麦迪逊分校进行的一学期的研究生讲座。由于这本专著的目的是对临界点理论中的主题进行统一的描述，因此增加了相当数量的新材料。其中一些以前从未发表过。这本书既对跟踪新结果发展的研究人员感兴趣，也对寻求介绍这一理论的人感兴趣。主要结果被设计成尽可能独立的。为了方便读者，我们整理了一些初步的背景资料。值得特别感谢的是，以下人员在帮助准备本书方面发挥了直接作用。L·尼伦伯格教授，十年前，当我访问库兰特数学科学研究所时，他第一次向我介绍了这个领域。A.Granas教授，他邀请我在1983年蒙特利尔的SMS上做一系列演讲，然后是上面的笔记，作为手稿的一部分的初级版本，这些手稿发表在SMS集合中。P·拉比诺维茨教授，他在学期中给了我极大的鼓励，并邀请我教授一个学期的研究生课程，之后课堂讲稿成为这本书部分内容的第二版。A.巴赫里和H.Brezis教授，他们建议在Birkhiiuser系列中出版这本书。
The book is based on my lecture notes" Infinite dimensional Morse theory and its applications", 1985, Montreal, and one semester of graduate lectures delivered at the University of Wisconsin, Madison, 1987. Since the aim of this monograph is to give a unified account of the topics in critical point theory, a considerable amount of new materials has been added. Some of them have never been published previously. The book is of interest both to researchers following the development of new results, and to people seeking an introduction into this theory. The main results are designed to be as self-contained as possible. And for the reader's convenience, some preliminary background information has been organized. The following people deserve special thanks for their direct roles in help ing to prepare this book. Prof. L. Nirenberg, who first introduced me to this field ten years ago, when I visited the Courant Institute of Math Sciences. Prof. A. Granas, who invited me to give a series of lectures at SMS, 1983, Montreal, and then the above notes, as the primary version of a part of the manuscript, which were published in the SMS collection. Prof. P. Rabinowitz, who provided much needed encouragement during the academic semester, and invited me to teach a semester graduate course after which the lecture notes became the second version of parts of this book. Professors A. Bahri and H. Brezis who suggested the publication of the book in the Birkhiiuser series.