Variational Methods, Lusternik-Schnirelman Theory and Applications

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.

Autorentext
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).