Homoclinic orbits for first order Hamiltonian systems with some twist conditions |
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Authors: | Yuan Shan |
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Affiliation: | School of Mathematics and Statistics, Nanjing Audit University, Nanjing 210029, P. R. China |
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Abstract: | In this paper, we study the nonperiodic first-order Hamiltonian system ?= JL(t)u + JH' (t, u), where H ∈ C1(R × R2n). With some assumptions on L, the corresponding Hamiltonian operator has only discrete spectrum. By using the index theory for self-adjoint operator equation, we establish the existence of multiple homoclinic orbits for the asymptotically quadratic nonlinearty satisfying some twist conditions between infinity and origin. |
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Keywords: | Homoclinic solutions first order Hamiltonian system index theory twist conditions |
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