Recurrent Solutions of a Nonautonomous Modified Swift-Hohenberg Equation

Jintao Wang, Lu Yang, Jinqiao Duan

We consider recurrent solutions of the nonautonomous modified Swift-Hohenberg equation $$u_t+{\Delta }^{2}u+2\Delta u+au+b|\nabla u{|}^2+u^3=g(t,x).$$ We employ Conley index theory to show that, if…