Variational Methods, Lusternik-Schnirelman Theory and Applications: Critical point theory and Minmax methods - Softcover

Degla, Guy; Okpala, Mmaduabuchi E.

Softcover

ISBN 10: 365927383X ISBN 13: 9783659273834

Publisher: LAP LAMBERT Academic Publishing, 2012

Synopsis

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.

About this title

About the Author

PhD Functional Analysis and Applications, SISSA, Trieste, Italy.Researcher at the African University of Science and Technology (AUST), Abuja, Nigeria, and at the Institut de Mathematiques et de Sciences Physiques (IMSP), Porto-Novo, Benin.Joint Project with M.E. Okpala (Teaching Assistant, AUST).

Edition details

• Publisher: LAP LAMBERT Academic Publishing
• Publication date: 2012
• ISBN 10: 365927383X
• ISBN 13: 9783659273834
• Binding: Paperback
• Language: English
• Number of pages: 76