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This unique book focuses on critical point theory for strongly indefinite functionals in order to deal with nonlinear variational problems in areas such as physics, mechanics and economics. With the original ingredients of Lipschitz partitions of unity of gage spaces (nonmetrizable spaces), Lipschitz normality, and sufficient conditions for the normality, as well as existence-uniqueness of flow of ODE on gage spaces, the book presents for the first time a deformation theory in locally convex topological vector spaces. It also offers satisfying variational settings for homoclinic-type solutions to Hamiltonian systems, Schroedinger equations, Dirac equations and diffusion systems, and describes recent developments in studying these problems. The concepts and methods used open up new topics worthy of in-depth exploration, and link the subject with other branches of mathematics, such as topology and geometry, providing a perspective for further studies in these areas. The analytical framework can be used to handle more infinite-dimensional Hamiltonian systems.
Variational Methods For Strongly Indefinite Problems
Lipschitz Partitions of Unity (Lipschitz Normality, Sufficient Conditions of the Normal Gage Space, Flow of ODE on Gage Spaces); Deformations on Locally Convex Topological Vector Spaces; Critical Point Theorems; Homoclinics in Hamiltonian Systems (Spectrum of the Hamiltonian Operator, Variational Setting, Linking Structure, the (C) Sequences, Existence and Multiplicity); Standing Waves of Schrodinger Equations; Solutions of Nonlinear Dirac Equations; Solutions of Systems of Diffusion Equations.