Oscillations of noncoercive superquadratic Hamiltonian systems. (Oscillations de systèmes hamiltoniens surquadratiques non coercitifs.) (French) Zbl 0828.70011
The Hamiltonian system is considered \(\dot r = {\partial H \over \partial p} (r,p)\), \(\dot p = - {\partial H \over \partial r} (r,p)\), where \(H(r,p) = f(|p - Ar |)\), \(r,p \in \mathbb{R}^n\), and the function \(f : \mathbb{R} \to \mathbb{R}\) is noncoercive and superquadratic. The existence of a nonconstant \(T\)-periodic solution is proved.
Reviewer: N.A.Lar’kin (Maringa)
MSC:
| 70H05 | Hamilton’s equations |
| 34C25 | Periodic solutions to ordinary differential equations |
| 37J99 | Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems |
