On the existence of Hamiltonian paths connecting Lagrangian submanifolds

Abstract

We use a new variational method --based on the theory of anti-selfdual Lagrangians developed in [2] and [3]-- to establish the existence of solutions of convex Hamiltonian systems that connect two given Lagrangian submanifolds in ${\mathbb{R}}^{2N}$. We also consider the case where the Hamiltonian is only semi-convex. A variational principle is also used to establish existence for the corresponding Cauchy problem. The case of periodic solutions will be considered in a forthcoming paper [5].

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References in corpus (1)

• Anti-selfdual Lagrangians: Variational resolutions of non self-adjoint equations and dissipative evolutions

Cited by in corpus (1)

• Selfdual Variational Principles for Periodic Solutions of Hamiltonian and Other Dynamical Systems