Abstract
In this paper, we prove a Hopf bifurcation theorem for second-order semi-linear equations involving non-densely defined operators. Here, we use the Crandall and Rabinowitz’s approach based on a suitable application of the implicit function theorem. As a special case, we obtain the existence of periodic wave trains for the so-called Gurtin–MacCamy problem arising in population dynamics and that couples both spatial diffusion and age structure.
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Ducrot, A., Kang, H. & Magal, P. Hopf bifurcation theorem for second-order semi-linear Gurtin–MacCamy equation. J. Evol. Equ. 22, 72 (2022). https://doi.org/10.1007/s00028-022-00833-3
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DOI: https://doi.org/10.1007/s00028-022-00833-3