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Homoclinic orbits for first order periodic Hamiltonian systems with spectrum point zero

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  • In this paper, we study the existence and multiplicity of homoclinic orbits for a class of first order periodic Hamiltonian systems. By applying two recent critical point theorems for strongly indefinite functionals, we establish some new criteria to guarantee that Hamiltonian systems, with asymptotically quadratic terms and spectrum point zero, have at least one and infinitely many homoclinic orbits under certain conditions.
    Mathematics Subject Classification: Primary: 58E05, 70H05; Secondary: 37J45.

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