Recurrent Solutions of a Nonautonomous Modified Swift-Hohenberg Equation
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摘要
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.
论文关键词：Modified Swift-Hohenberg equations,Nonautonomous dynamical systems,Recurrent functions,Conley index,Gradient systems
论文评审过程：Received 9 July 2019, Revised 17 February 2020, Accepted 22 March 2020, Available online 14 April 2020, Version of Record 14 April 2020.
论文官网地址：https://doi.org/10.1016/j.amc.2020.125270
