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Ground state for a fractional reaction-diffusion system
Peng Chen,Zhijie Cao,Sitong Chen,Xianhua Tang
Keywords:Reaction-diffusion system; Ground states; Strongly indefinite functional
Abstract:
      In this paper, we prove the existence of the ground state of a strongly indefinite fractional reaction-diffusion system based on the Non-Nehari method established by Tang-Chen-Lin-Yu [J. Differ. Equ. 268 (2020) 4663-4690]. In particular, neither any monotonicity condition nor any Ambrosetti-Rabinowitz growth condition is required. To our knowledge, this is the first result about the ground states with the strongly indefinite case for fractional reaction-diffusion system.