莫尔斯电码
莫尔斯理论
对偶(序理论)
牙石(牙科)
点(几何)
多样性(控制论)
微扰理论(量子力学)
非线性系统
数学
摄动(天文学)
偏微分方程
应用数学
数理经济学
计算机科学
数学分析
纯数学
几何学
物理
电信
量子力学
医学
统计
牙科
标识
DOI:10.1017/cbo9780511551703
摘要
The calculus of variations has been an active area of mathematics for over 300 years. Its main use is to find stable critical points of functions for the solution of problems. To find unstable values, new approaches (Morse theory and min-max methods) were developed, and these are still being refined to overcome difficulties when applied to the theory of partial differential equations. Here, Professor Ghoussoub describes a point of view that may help when dealing with such problems. Building upon min-max methods, he systematically develops a general theory that can be applied in a variety of situations. In so doing he also presents a whole array of duality and perturbation methods. The prerequisites for following this book are relatively few; an appendix sketching certain methods in analysis makes the book reasonably self-contained. Consequently, it should be accessible to all mathematicians, pure or applied, economists and engineers working in nonlinear analysis or optimization.
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