journal6 ›› 2011, Vol. 32 ›› Issue (3): 14-18.

• Mathematics • Previous Articles     Next Articles

Homoclinic Orbits for Second Order Self-Adjoint Difference System with a Change of Sign in the Potential

  

  1. (1.Department of Mathematics and Computer Science,Jishou University,Jishou 416000,Hunan China;2.School of Mathematical Sciences and Computing Technology,Central South University,Changsha 410083,China)
  • Online:2011-05-25 Published:2012-04-08
  • About author:HE Xiao-fei(1971-),male,was born in Xinshao City,Hunan Province,Ph.D.student,associate professor at the College of Mathematical and Computer Science,Jishou University;research area is stability and bifurcation theory of differential equations with delays.
  • Supported by:

    Scientific Research Fund of Hunan Province (09JJ6010)

Abstract: The authors we study the existence of nontrivial homoclinic orbits of the second self-adjoint difference system Δ2 u(t-1)-q(t)u(t)+V(t,u(t))=0t∈Z,u∈Rm.Under superquadratic conditions,by using the Mountain Pass Theorem and the Symmetric Mountain Pass Theorem,some existence theorems are established for the existence of homoclinic orbits for the above nonautonomous Hamiltonian systems with a change of sign in the potential.

Key words: homoclinic orbits, difference system, Mountain Pass Theorem

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