# American Institute of Mathematical Sciences

August  2013, 33(8): 3807-3824. doi: 10.3934/dcds.2013.33.3807

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

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

Received  September 2012 Revised  November 2012 Published  January 2013

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.
Citation: Juntao Sun, Jifeng Chu, Zhaosheng Feng. Homoclinic orbits for first order periodic Hamiltonian systems with spectrum point zero. Discrete & Continuous Dynamical Systems, 2013, 33 (8) : 3807-3824. doi: 10.3934/dcds.2013.33.3807
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