Multibump solutions for a class of Lagrangian systems slowly oscillating at infinity

  • Francesca Alessio

    Dipartimento di Matematica del Politecnico di Torino, Corso Duca degli Abruzzi, 24, I-10129 Torino, Italy
  • Piero Montecchiari

    Dipartimento di Matematica dell’Università di Trieste, Piazzale Europa, 1, I-34100 Trieste, Italy

Abstract

We prove the existence of infinitely many homoclinic solutions for a class of second order hamiltonian systems of the form where is superquadratic and , as . In fact we prove that such a kind of systems admit a “multibump” dynamics.

Résumé

On montre l’existence d’une infinité de solutions homoclines d’une classe de systèmes hamiltoniens du second ordre de la forme est superquadratique et , quand . On montre en particulier que cette famille des systèmes admet une dynamique “multi-bosses”.

Cite this article

Francesca Alessio, Piero Montecchiari, Multibump solutions for a class of Lagrangian systems slowly oscillating at infinity. Ann. Inst. H. Poincaré Anal. Non Linéaire 16 (1999), no. 1, pp. 107–135

DOI 10.1016/S0294-1449(99)80009-2