Bulletin of the
Korean Mathematical Society BKMS

Applying the Lyapunov--Schmidt reduction, we consider \linebreak 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.

Keywords: Generalized Swift--Hohenberg equations, bifurcating periodic solutions, Lyapunov--Schmidt reduction

MSC numbers: Primary 35B35

Supported by: This work was financially supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (No. 2022R1F1A1074414).