• Title/Summary/Keyword: Lyapunov-Schmidt reduction

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STABILITY OF BIFURCATING STATIONARY PERIODIC SOLUTIONS OF THE GENERALIZED SWIFT-HOHENBERG EQUATION

  • Soyeun, Jung
    • Bulletin of the Korean Mathematical Society
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    • v.60 no.1
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    • pp.257-279
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    • 2023
  • Applying the Lyapunov-Schmidt reduction, we consider spectral stability of small amplitude stationary periodic solutions bifurcating from an equilibrium of the generalized Swift-Hohenberg equation. We follow the mathematical framework developed in [15, 16, 19, 23] to construct such periodic solutions and to determine regions in the parameter space for which they are stable by investigating the movement of the spectrum near zero as parameters vary.