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Homoclinic solutions for a second-order Hamiltonian system with a positive semi-definite matrix

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  • Sun, Juntao
  • Wu, Tsung-fang

Abstract

In this paper, we study homoclinic solutions for second-order Hamiltonian systems u¨-L(t)u+Wu(t,u)=0, where L(t) is allowed to be a positive semi-definite symmetric matrix for all t∈R, and W∈C1(R×RN,R) is an indefinite potential satisfying asymptotically quadratic condition at infinity on u. We obtain some new results on the existence and multiplicity of homoclinic solutions for second-order systems. The proof is based on variational methods.

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  • Sun, Juntao & Wu, Tsung-fang, 2015. "Homoclinic solutions for a second-order Hamiltonian system with a positive semi-definite matrix," Chaos, Solitons & Fractals, Elsevier, vol. 76(C), pages 24-31.
    • Handle: RePEc:eee:chsofr:v:76:y:2015:i:c:p:24-31
    DOI: 10.1016/j.chaos.2015.03.004
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    References listed on IDEAS

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    1. Lv, Ying & Tang, Chun-Lei, 2013. "Homoclinic orbits for second-order Hamiltonian systems with subquadratic potentials," Chaos, Solitons & Fractals, Elsevier, vol. 57(C), pages 137-145.
    2. Ying Lv & Chun-Lei Tang, 2013. "Existence and Multiplicity of Homoclinic Orbits for Second-Order Hamiltonian Systems with Superquadratic Potential," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-12, February.
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    Cited by:

    1. Wang, Xiaoping, 2016. "Infinitely many homoclinic solutions for a second-order Hamiltonian system with locally defined potentials," Chaos, Solitons & Fractals, Elsevier, vol. 87(C), pages 47-50.

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    1. Wang, Xiaoping, 2016. "Infinitely many homoclinic solutions for a second-order Hamiltonian system with locally defined potentials," Chaos, Solitons & Fractals, Elsevier, vol. 87(C), pages 47-50.

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