English

Some Inequalities Satisfied by Periodical Solutions of Multi-Time Hamilton Equations

Dynamical Systems 2007-05-23 v1 Analysis of PDEs

Abstract

The objective of this paper is to find some inequalities satisfied by periodical solutions of multi-time Hamilton systems, when the Hamiltonian is convex. To our knowledge, this subject of first-order field theory is still open. Section 1 recall well-known facts regarding the equivalence between Euler-Lagrange equations and Hamilton equations and analyses the action that produces multi-time Hamilton equations, emphasizing the role of the polysymplectic structure. Section 2 extends two inequalities of [21] from a cube to parallelipiped and proves two inequalityes concerning multiple periodical solutions of multi-time Hamilton equations.

Keywords

Cite

@article{arxiv.math/0510557,
  title  = {Some Inequalities Satisfied by Periodical Solutions of Multi-Time Hamilton Equations},
  author = {Iulian Duca and Constantin Udriste},
  journal= {arXiv preprint arXiv:math/0510557},
  year   = {2007}
}

Comments

14 pages, Key words: multi-time Hamilton action, Wirtinger inequality, convex Hamiltonian; Communicated at 5-th Conference of Balkan Society of Geometers (5-th Conference on Differential Geometry), August 28- September 2, 2005, Mangalia, Romania