  In this paper we consider the Arnold conjecture on the Lagrangian
intersections of some closed Lagrangian submanifold of a closed symplectic
manifold with its image of a Hamiltonian diffeomorphism. We prove that if the
Hofer's symplectic energy of the Hamiltonian diffeomorphism is less than a
topology number defined by the Lagrangian submanifold, then the Arnold
conjecture is true in the degenerated (non-transversal) case.
