Homoclinic orbits for  first order periodicHamiltonian systems with spectrum point zero

Juntao Sun; Jifeng Chu; Zhaosheng Feng

doi:10.3934/dcds.2013.33.3807

Article Contents

2013, Volume 33, Issue 8: 3807-3824. Doi: 10.3934/dcds.2013.33.3807

This issue Previous Article A blow-up criterion for the 3D compressible magnetohydrodynamics in terms of density Next Article Addendum to: Symbolic dynamics for the $N$-centre problem at negative energies

Homoclinic orbits for first order periodic Hamiltonian systems with spectrum point zero

1.
School of Science, Shandong University of Technology, Zibo 255049
2.
Department of Mathematics, College of Science, Hohai University, Nanjing 210098
3.
Department of Mathematics, University of Texas-Pan American, Edinburg, TX 78539

Received: August 31, 2012

Revised: October 31, 2012

Published: July 2013

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Abstract

In this paper, we study the existence and multiplicity of homoclinic orbits for a class of first order periodic Hamiltonian systems. By applying two recent critical point theorems for strongly indefinite functionals, we establish some new criteria to guarantee that Hamiltonian systems, with asymptotically quadratic terms and spectrum point zero, have at least one and infinitely many homoclinic orbits under certain conditions.

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Mathematics Subject Classification: Primary: 58E05, 70H05; Secondary: 37J45.

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