Origin and evolution of the Palais-Smale condition in critical point theory

被引:21
|
作者
Mawhin, Jean [1 ]
Willem, Michel [1 ]
机构
[1] Catholic Univ Louvain, Dept Math, B-1348 Louvain, Belgium
关键词
Condition (C); Palais-Smale condition; critical point theory; minimax theorems; EKELANDS VARIATIONAL PRINCIPLE; BOUNDARY-VALUE PROBLEM; MOUNTAIN PASS; LUSTERNIK-SCHNIRELMAN; MULTIPLE SOLUTIONS; POSITIVE SOLUTIONS; HILBERT SPACE; EQUATIONS; MORSE; FUNCTIONALS;
D O I
10.1007/s11784-010-0019-7
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In 1963-64, Palais and Smale have introduced a compactness condition, namely condition (C), on real functions of class C-1 defined on a Riemannian manifold modeled upon a Hilbert space, in order to extend Morse theory to this frame and study nonlinear partial differential equations. This condition and some of its variants have been essential in the development of critical point theory on Banach spaces or Banach manifolds, and are referred as Palais-Smale-type conditions. The paper describes their evolution.
引用
收藏
页码:265 / 290
页数:26
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