Nonstationary homoclinic orbit for an infinite-dimensional fractional reaction-diffusion system

<p style='text-indent:20px;'>This paper study nonstationary homoclinic-type solutions for a fractional reaction-diffusion system with asymptotically linear and local super nonlinearity. The resulting problem engages two major difficulties: one is that the associated functional strongly indefinite, second lies in verifying link geometry showing boundedness of Cerami sequences when nonlinearity not quadratic at infinity globally. These enable us to develop direct approach new tricks overcome difficulties. We establish existence homoclinic orbit under some weak assumptions on nonlinearity.</p>