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Ground state homoclinic orbits for a class of asymptotically periodic second-order Hamiltonian systems

  • * Corresponding author: Chun-Lei Tang

    * Corresponding author: Chun-Lei Tang

The first author is supported by Fundamental Research Funds for the Central Universities (XDJK2020B051) and National Natural Science Foundation of China(No. 11601438, 11971393)

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  • In this paper, we consider a class of second-order Hamiltonian systems of the form

    $ \ddot{u}(t)-L(t) u(t)+\nabla W(t,u(t)) = 0 $

    where $ L:R\rightarrow R^{N^2} $ and $ W \in C^1(R\times R^N, R) $ are asymptotically periodic in $ t $ at infinity. Under the reformative perturbation conditions and weaker superquadratic conditions on the nonlinearity, the existence of a ground state homoclinic orbit is established. The main tools employed here are the local mountain pass theorem and the concentration-compactness principle.

    Mathematics Subject Classification: Primary: 37J45, 37K05; Secondary: 58E05.

    Citation:

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