Open AccessNonstationary homoclinic orbit for an infinite-dimensional fractional reaction-diffusion system
Author(s) -
Chen Peng,
Linfeng Mei,
Xianhua Tang
Publication year - 2022
Publication title -
discrete and continuous dynamical systems. series b
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.864
H-Index - 53
eISSN - 1553-524X
pISSN - 1531-3492
DOI - 10.3934/dcdsb.2021279
Subject(s) - homoclinic orbit , orbit (dynamics) , nonlinear system , infinity , mathematics , reaction–diffusion system , diffusion , quadratic equation , mathematical analysis , physics , geometry , bifurcation , quantum mechanics , engineering , aerospace engineering
This paper study nonstationary homoclinic-type solutions for a fractional reaction-diffusion system with asymptotically linear and local super linear nonlinearity. The resulting problem engages two major difficulties: one is that the associated functional is strongly indefinite, the second lies in verifying the link geometry and showing the boundedness of Cerami sequences when the nonlinearity is not super quadratic at infinity globally. These enable us to develop a direct approach and new tricks to overcome the difficulties. We establish the existence of homoclinic orbit under some weak assumptions on nonlinearity.