The Hopf Bifurcation Theorem in Hilbert Spaces for Abstract Semilinear Equations

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