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Recurrent Solutions of a Nonautonomous Modified Swift-Hohenberg Equation

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  • Wang, Jintao
  • Yang, Lu
  • Duan, Jinqiao

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.

Suggested Citation

  • Wang, Jintao & Yang, Lu & Duan, Jinqiao, 2020. "Recurrent Solutions of a Nonautonomous Modified Swift-Hohenberg Equation," Applied Mathematics and Computation, Elsevier, vol. 379(C).
    • Handle: RePEc:eee:apmaco:v:379:y:2020:i:c:s0096300320302393
    DOI: 10.1016/j.amc.2020.125270
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    References listed on IDEAS

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    1. Desheng Li & Jinying Wei & Jintao Wang, 2013. "On the Dynamics of Abstract Retarded Evolution Equations," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-9, November.
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