5 research outputs found

    A Note on Homoclinic Orbits for Second Order Hamiltonian Systems

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    In this paper, we study the existence for the homoclinic orbits for the second order Hamiltonian systems. Under suitable conditions on the potential VV, we apply the direct method of variations and the Fourier analysis to prove the existence of homoclinc orbits

    Hyperbolic Orbits for a Class of Singular Hamiltonian Systems

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    The existence of hyperbolic orbits is proved for a class of singular Hamiltonian systems u¨(t)+∇V(u(t))=0\ddot{u}(t)+\nabla V(u(t))=0 by taking limit for a sequence of periodic solutions which are the variational minimizers of Lagrangian actions
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