Recurrent Solutions of a Nonautonomous Modified Swift-Hohenberg Equation

We consider recurrent solutions of the nonautonomous modified Swift-Hohenberg equation $u_t+Δ^2u+2Δu+au+b|\nabla u|^2+u^3=g(t,x).$ We employ Conley index theory to show that, if the forcing $g:\mathbb{R}\rightarrow L^2(Ω)$ is a recurrent function, then there are at least two recurrent solutions in $H_0^2(Ω)$ under appropriate assumptions on the parameters $a$, $b$ and $g$.

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