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Zbl 0761.34017
Fan, Xianling
A Viterbo-Hofer-Zehnder type result for Hamiltonian inclusions. (English)
[J] Ann. Fac. Sci. Toulouse, V. Sér., Math. 12, No.3, 365-372 (1991). ISSN 0240-2955

Let $H:\bbfR\sp{2N}\to\bbfR$ be a locally Lipschitz function, $\Sigma\sb c=H\sp{-1}(c)$ be a nonempty compact set and $0\not\in\partial H(x)$ for $x\in\Sigma\sb c$ where $\partial H$ is a Clarke generalized gradient of $H$. Let $J$ denote the standard $2N\times 2N$ symplectic matrix, then for any $\delta>0$ the Hamiltonian inclusion $\dot X\in J\partial H(x)$ has a conservative periodic solution $x$ such that $H(x(t))\equiv c'\in(c-\delta,c+\delta)$ for all $t$.
[V.V.Obukhovskij (Voronezh)]

MSC 2000:: *34A60 ODE with multivalued right-hand sides
37J99 Finite-dimensional Hamiltonian etc. systems
37G99 Bifurcation theory
34C25 Periodic solutions of ODE

Keywords: differential inclusion; Hamiltonian inclusion; conservative periodic solution

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