Timoumi, Mohsen Subharmonics of convex non-coercive Hamiltonian systems. (English) Zbl 0785.58040 Collect. Math. 43, No. 1, 63-69 (1992). The Hamiltonian system under consideration reads \[ \dot u=JH'(t,u),\tag{H} \] where \(H(t,r,p)=f(| p-A(t)r|)\), \(t\in\mathbb{R}^ 1\); \(r,p\in\mathbb{R}^ n\), \(f:\mathbb{R}_ +\to\mathbb{R}_ +\) is a nondecreasing convex function and \(A:\mathbb{R}^ 1\to{\mathfrak M}(n,\mathbb{R}^ 1)\) is a continuous \(T\)-periodic function.The following statement is proved:Theorem. The Hamiltonian system (H) has, for each \(k\in\mathbb{N}^*\), a \(kT\)-periodic solution \(u_ k=(r_ k,p_ k)\) such that(a) \(\| p_ k-Ar_ k\|_ \infty\to\infty\) as \(k\to\infty\),(b) \(kT\) is the minimal period of \(u_ k\) for any sufficiently large prime number \(k\). Reviewer: J.Andres (Olomouc) Cited in 1 Document MSC: 37G99 Local and nonlocal bifurcation theory for dynamical systems Keywords:subharmonics; Hamiltonian system PDFBibTeX XMLCite \textit{M. Timoumi}, Collect. Math. 43, No. 1, 63--69 (1992; Zbl 0785.58040) Full Text: EuDML