Bifurcation theory : an introduction with applications to PDEs
Bifurcation theory : an introduction with applications to PDEs
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DOI：
10.1007/b97365
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发表时间：
2004
期刊：
影响因子：
--
通讯作者：
H. Kielhöfer
中科院分区：
文献类型：
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作者：
H. Kielhöfer
在过去的三十年里，分支理论已经发展成为一个成熟的、充满活力的数学分支。这本书给出了一个统一的介绍在一个抽象的设置的主要定理在分歧理论，以及最近和鲜为人知的结果。它涵盖了在无限维Banach空间中作用的算子的单参数分支的局部和全局理论，并展示了如何将该理论应用于涉及偏微分方程的问题。除了存在性，定性性质，如稳定性和节点结构的分歧解决方案进行了深入的处理。这卷将作为一个重要的参考数学家，物理学家，和理论倾向的工程师工作在分歧理论及其应用偏微分方程。
In the past three decades, bifurcation theory has matured into a well-established and vibrant branch of mathematics. This book gives a unified presentation in an abstract setting of the main theorems in bifurcation theory, as well as more recent and lesser known results. It covers both the local and global theory of one-parameter bifurcations for operators acting in infinite-dimensional Banach spaces, and shows how to apply the theory to problems involving partial differential equations. In addition to existence, qualitative properties such as stability and nodal structure of bifurcating solutions are treated in depth. This volume will serve as an important reference for mathematicians, physicists, and theoretically-inclined engineers working in bifurcation theory and its applications to partial differential equations.