Subharmonic solutions of a nonconvex noncoercive hamiltonian system

Najeh Kallel; Mohsen Timoumi

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In this work we will consider a class of second order perturbed Hamiltonian systems of the form $q ̈ + V_{q} (t, q) = f (t)$ , where t ∈ ℝ, q ∈ ℝⁿ, with a superquadratic growth condition on a time periodic potential V: ℝ × ℝⁿ → ℝ and a small aperiodic forcing term f: ℝ → ℝⁿ. To get an almost homoclinic solution we approximate the original system by time periodic ones with larger and larger time periods. These approximative systems admit periodic solutions, and an almost homoclinic solution for the original system...

Periodic solutions for some nonautonomous $p (t)$ -Laplacian Hamiltonian systems

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In this paper, we deal with the existence of periodic solutions of the $p (t)$ -Laplacian Hamiltonian system $\{\begin{matrix} \frac{d}{d t} (| \dot{u} (t) |^{p (t) - 2} \dot{u} (t)) = \nabla F (t, u (t)) a.e. t \in [0, T], \\ u (0) - u (T) = \dot{u} (0) - \dot{u} (T) = 0 . \end{matrix}$ Some new existence theorems are obtained by using the least action principle and minimax methods in critical point theory, and our results generalize and improve some existence theorems.