The Hopf bifurcation theorem in Hilbert spaces for abstract semilinear equations

Tadashi Kawanago

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arXiv · 1803.11446

The Hopf bifurcation theorem in Hilbert spaces for abstract semilinear equations

Tadashi Kawanago

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Abstract

We prove a Hopf bifurcation theorem in Hilbert spaces for abstract semilinear equations, which improves a classical result by Crandall and Rabinowitz in the case where basic spaces are Hilbert spaces. Actually, our theorem does not need any compactness conditions, which leads to wider applications. In particular, our theorem can be applied to semilinear equations in unbounded domains of $\mathbb{R}^n$.

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Tadashi Kawanago. 2018-03-30. The Hopf bifurcation theorem in Hilbert spaces for abstract semilinear equations. https://arxiv.org/abs/1803.11446

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