Introduction to Functional Differential Equations
Introduction to Functional Differential Equations
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DOI：
10.1007/978-1-4612-4342-7
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发表时间：
1993-10
期刊：
影响因子：
--
通讯作者：
J. Hale;S. Lunel
中科院分区：
文献类型：
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作者：
J. Hale;S. Lunel
目前的书建立在J.黑尔的早期工作，“泛函微分方程理论”出版于1977年。我们试图保持那本书的精神，并保留了大约三分之一的材料完好无损。一个主要的变化是对迟滞型和中立型泛函微分方程的线性方程组（第6~ 9章）有了全新的表述。对耗散系统理论（第4章）和全局牵引器理论以及平衡点和周期轨道附近的不变流形理论（第10章）进行了全面的改进。一个更完整的理论中立方程被提出（见第1、2、3、9和10章）。第12章是全新的，包含了对当前研究主题的指导。在关于补充说明的章节中，我们引用了许多最近的文献，但是，当然，不是几乎全部，因为这个主题是如此广泛。杰克·k·黑尔会发生m . Verduyn卢奈尔内容前言 ............................................................v的介绍 ..................................1 ....................1. 线性微分差分方程..............11……1.1微分和差分方程 ....................11……1.2迟滞微分差分方程................13……1.3 x(¢f指数的估计 ).....................15 ..........1.4特征方程 ........................17 ............1.5基本解决方案 ..........................18 ............1.6 variation-of-constants公式 .............................23 1。7中性微分差分方程.................25……1.8补充的话 ...........................34 .............2. 泛函微分方程：基本理论........38 . .2.1定义的延迟方程 ......................38……2.2存在、唯一性和持续依赖..........39……2.3持续的解决方案 ..........................44 ............
The present book builds upon an earlier work of J. Hale," Theory of Func tional Differential Equations" published in 1977. We have tried to maintain the spirit of that book and have retained approximately one-third of the material intact. One major change was a complete new presentation of lin ear systems (Chapters 6~ 9) for retarded and neutral functional differential equations. The theory of dissipative systems (Chapter 4) and global at tractors was completely revamped as well as the invariant manifold theory (Chapter 10) near equilibrium points and periodic orbits. A more complete theory of neutral equations is presented (see Chapters 1, 2, 3, 9, and 10). Chapter 12 is completely new and contains a guide to active topics of re search. In the sections on supplementary remarks, we have included many references to recent literature, but, of course, not nearly all, because the subject is so extensive. Jack K. Hale Sjoerd M. Verduyn Lunel Contents Preface............................................................ v Introduction.................................. 1.................... 1. Linear differential difference equations.............. 11...... 1.1 Differential and difference equations.................... 11........ 1.2 Retarded differential difference equations................ 13....... 1.3 Exponential estimates of x (¢, f)..................... 15.......... 1.4 The characteristic equation........................ 17............ 1.5 The fundamental solution.......................... 18............ 1.6 The variation-of-constants formula............................. 23 1. 7 Neutral differential difference equations................. 25....... 1.8 Supplementary remarks........................... 34............. 2. Functional differential equations: Basic theory........ 38.. 2.1 Definition of a retarded equation...................... 38......... 2.2 Existence, uniqueness, and continuous dependence.......... 39... 2.3 Continuation of solutions.......................... 44............