2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/67014In 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.18 pages, submittedSymplectic Geometry58F05;58E05; 34C25; 58F10text