Variational Methods, Lusternik-Schnirelman Theory and Applications Год выпуска: 2012Автор: Guy Degla and Mmaduabuchi E. OkpalaИздательство: LAP Lambert Academic PublishingСтраниц: 76ISBN: 9783659273834Описание This project concerns mainly the study of the critical point Theory of Lusternik-Schnirelman which relies deeply on concepts from Nonlinear Analysis, Topology and Geometry, and has numerous applications to Variational Problems and Partial Differential Equations (PDEs) of variational nature. We first survey the general variational principles and provide the underlying abstract setting need for the theory and its applications. Secondly we present a very successful min-max method (Ambrosetti-Rabinowitz Mountain-pass theorem) based on the Palais-Smale (compactness) condition and followed by examples. Afterwards we introduce progressively the Lusternik-Schrenirelman theories in Euclidean spaces (finite dimensional case) and in Hilbert spaces as well as in uniformly convex Banach spaces (infinite dimensional cases), along with applications.
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Дима, 05.02 марин спасибо за дипломный проект
