Periodic solutions for a class of sublinear second order Hamiltonian system

  • Fathi Khelifi
  • Mohsen Timoumi
Keywords: Periodic solutions, Hamiltonian systems, saddle point Theorem, sublinear nonlinearity.


In this paper, we study the existence of periodic solutions for the nonautonomous second order Hamiltonian system
\ddot{u}(t)+Au(t)-\nabla F(t,u(t))=e(t),
under some new sublinear nonlinearity conditions. For the resolution, we apply the minimax methods in critical point theory to the least action integral.