Sunto
Si dimostra l'esistenza di soluzioni multiple per l'equazione Lu=A(u) ove L è un operatore indefinito ed autoaggiunto in uno spazio di Hilbert; A è un operatore variazionale, monotono, dispari che «cresce» in maniera opportuna più che linearmente per ∥u∥ → ∞. Dal suddetto risultato si deduce, tra l'altro, l'esistenza di soluzioni periodiche multiple per sistemi hamiltoniani ed equazioni delle onde non lineari sulla sfera n-dimensionale Sn.
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Work partially supported by C.N.R. and M.P.I.
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Benci, V., Fortunato, D. The dual method in critical point theory. Multiplicity results for indefinite functional. Annali di Matematica pura ed applicata 132, 215–242 (1982). https://doi.org/10.1007/BF01760982
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DOI: https://doi.org/10.1007/BF01760982