Abstract
The aim of this paper is to study ground state solution of the first order discrete Hamiltonian systems. The resulting problem engages two major difficulties: one is that the associated functional is strongly indefinite, the second is that, due to the lack of strict monotone type condition which is very crucial in strongly indefinite problem, many effective methods cannot be applied to it. Based on the recent work Chen et al. (2011); Guo and Yu (2003), for the first time, we obtain the existence of ground state solutions via non-Nehari method developed recently Qin et al. (2021); Tang et al. (2020) under some weaker assumptions.
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