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New existence and multiplicity results of homoclinic orbits for a class of second order Hamiltonian systems

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  • Ye, Yiwei
  • Tang, Chun-Lei

Abstract

In this paper, we study the nonperiodic second order Hamiltonian systemsu¨(t)-λL(t)u(t)+∇W(t,u(t))=0,∀t∈R,where λ⩾1 is a parameter, the matrix L(t) is not necessarily positive definite for all t∈R nor coercive. Replacing the Ambrosetti–Rabinowitz condition by general superquadratic assumptions, we establish the existence and multiplicity results for the above system when λ>1 large. We also consider the situation where W is a combination of subquadratic and superquadratic terms, and obtain infinitely many homoclinic solutions.

Suggested Citation

  • Ye, Yiwei & Tang, Chun-Lei, 2014. "New existence and multiplicity results of homoclinic orbits for a class of second order Hamiltonian systems," Chaos, Solitons & Fractals, Elsevier, vol. 69(C), pages 151-159.
    • Handle: RePEc:eee:chsofr:v:69:y:2014:i:c:p:151-159
    DOI: 10.1016/j.chaos.2014.09.016
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    References listed on IDEAS

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    1. Qi Wang & Qingye Zhang, 2012. "Homoclinic Orbits for Second-Order Hamiltonian Systems with Some Twist Condition," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-15, June.
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