Abstract
In this paper we consider the following Hamiltonian system
Under a new superquadratic assumption on the potential, we prove that (HS) has a sequence of subharmonics. This will be done using a minimax result in critical point theory. Also, we study the asymptotic behavior of these subharmonics and we establish the existence of a homoclinic orbit for (HS). Previous results in the topic, mainly those due to Rabinowitz and Tanaka, are significantly improved.
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Daouas, A. On the existence of periodic and homoclinic orbits for first order superquadratic Hamiltonian systems. Nonlinear Differ. Equ. Appl. 20, 1347–1364 (2013). https://doi.org/10.1007/s00030-012-0211-0
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DOI: https://doi.org/10.1007/s00030-012-0211-0