Abstract
Publisher Summary This chapter presents an introduction to variational methods for strongly indefinite functional, such as Φ and its applications to the Hamiltonian system (HS). The chapter discusses critical point theory, periodic solutions, and homoclinic solutions of HS. A unified approach is presented via a finite-dimensional reduction to show the existence of one solution and via a Galerkin-type method to find more solutions. The existence of periodic solutions near equilibria is concerned and the fixed energy problem is considered. Homoclinic solutions for HS with time-periodic Hamiltonian present a few basic existences and multiplicity results and discusses a relation to the Bernoulli shift and complicated dynamics.
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