Geodesic
Classic theorem by Lyapunov for differential equations in Hilbert spaces
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 2 (2008), pp. 6-12

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A theorem analogical to Lyapunov Classic Theorem is formulated for differential equations in Hilbert spaces. Example from the theory of partial differential equations is presented. The result automatically demonstrates the well-know conditions of continuum existence for periodic solutions of ordinary differential equations systems. Moreover, by applying the topological degree theory, these conditions can be set as less rigid than those formulated in Hopf Bifurcation Theory.
Keywords: Lyapunov theorem, Hilbert space, periodic solutions, Fredholm operator, a special nonequivalent substitution of variable. 
@article{VSGTU_2008_2_a0,
     author = {S. A. Vavilov and V. S. Fedotova},
     title = {Classic theorem by {Lyapunov} for differential equations in {Hilbert} spaces},
     journal = {Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences},
     pages = {6--12},
     publisher = {mathdoc},
     number = {2},
     year = {2008},
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     url = {http://geodesic.mathdoc.fr/item/VSGTU_2008_2_a0/}
}
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S. A. Vavilov; V. S. Fedotova. Classic theorem by Lyapunov for differential equations in Hilbert spaces. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 2 (2008), pp. 6-12. http://geodesic.mathdoc.fr/item/VSGTU_2008_2_a0/