Bull. Korean Math. Soc. 2023; 60(1): 257-279
Online first article January 26, 2023 Printed January 31, 2023
https://doi.org/10.4134/BKMS.b220116
Copyright © The Korean Mathematical Society.
Soyeun Jung
Kongju National University
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).
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