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Acta Applicandae Mathematicae

, Volume 110, Issue 3, pp 1353–1371 | Cite as

Homoclinic Orbits of Nonperiodic Super Quadratic Hamiltonian System

  • Jian Ding
  • Junxiang Xu
  • Fubao Zhang
Article

Abstract

This paper is concerned with solutions of the Hamiltonian system: \(\dot{u}=\mathcal{J}H_{u}(t,u)\) , where \(H(t,u)=\frac{1}{2}u\cdot Lu+W(t,u)\) with L being a 2N×2N symmetric matrix and WC 1(ℝ×ℝ2N ,ℝ) being super quadratic at infinity in u∈ℝ2N . We use variational methods to study this problem. By virtue of some auxiliary system related to the “limit equation” of the Hamiltonian system, we constructed linking levels of the variational functional Φ such that the minimax value E l based on the linking structure of Φ satisfies \(0<E_{l}<E_{l_{0}}\) , where \(E_{l_{0}}\) is the least action of the “limit equation”. Thus we can show the (PS) c -condition holds true for all \(c<E_{l_{0}}\) and consequently we obtain one solution of the Hamiltonian system.

Keywords

Hamiltonian system Super quadratic Least action solution (PS)c-condition Lions’ concentration compactness principle 

Mathematics Subject Classification (2000)

37K05 

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Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.Department of MathematicsSoutheast UniversityNanjingPeople’s Republic of China

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