Annali di Matematica Pura ed Applicata

, Volume 147, Issue 1, pp 21–72

Periodic solutions of convex autonomous Hamiltonian systems with a quadratic growth at the origin and superquadratic at infinity

  • Mario Girardi
  • Michele Matzeu
Article

Sunto

Dato un sistema Hamiltoniano, nel quale la funzione Hamiltoniana è la somma di un termine quadratico definito positivo e di un termine superquadratico convesso, si dimostra l'esistenza di soluzioni periodiche di periodo minimo T fissato, per ogni T ε (0, 2π/ΩN), dove ΩN è il massimo autovalore della forma quadratica. Si utilizzano alcune tecniche relative alla teoria dell'indice di Morse, introdutte in [13], [15], [16] ed una opportuna formulazione del principio di dualità di Clarke ed Ekeland (vedi [10], [11]).

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© Fondazione Annali di Matematica Pura ed Applicata 1985

Authors and Affiliations

  • Mario Girardi
    • 1
  • Michele Matzeu
    • 1
  1. 1.Dipartimento di MatematicaUniversità di Roma I, Città UniversitariaRomaItalia

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