Abstract
We consider recurrent solutions of the nonautonomous modified Swift-Hohenberg equationut+Δ2u+2Δu+au+b|∇u|2+u3=g(t,x).We employ Conley index theory to show that, if the forcing g:R→L2(Ω) is a recurrent function, then there are at least two recurrent solutions in H02(Ω) under appropriate assumptions on the parameters a, b and g.
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