We consider T-periodic parametrized retarded functional motion equations on (possibly) noncompact manifolds; that is, constrained second order retarded functional differential equations. For such equations, we prove a global continuation result for $T$-periodic solutions. The approach is topological and based on the degree theory for tangent vector fields as well as on the fixed point index theory. Our main theorem is a generalization to the case of retarded equations of an analogous result obtained by the last two authors for second order differential equations on manifolds. As corollaries we derive a Rabinowitz-type global bifurcation result and a Mawhin-type continuation principle. Finally, we deduce the existence of forced oscillations for the retarded spherical pendulum under general assumptions.
Global continuation of forced oscillations of retarded motion equations on manifolds / Benevieri, Pierluigi; Calamai, Alessandro; Furi, Massimo; Pera, Maria Patrizia. - In: JOURNAL OF FIXED POINT THEORY AND ITS APPLICATIONS. - ISSN 1661-7738. - STAMPA. - 16:(2015), pp. 273-300. [10.1007/s11784-015-0215-6]
Global continuation of forced oscillations of retarded motion equations on manifolds
BENEVIERI, PIERLUIGI;FURI, MASSIMO;PERA, MARIA PATRIZIA
2015
Abstract
We consider T-periodic parametrized retarded functional motion equations on (possibly) noncompact manifolds; that is, constrained second order retarded functional differential equations. For such equations, we prove a global continuation result for $T$-periodic solutions. The approach is topological and based on the degree theory for tangent vector fields as well as on the fixed point index theory. Our main theorem is a generalization to the case of retarded equations of an analogous result obtained by the last two authors for second order differential equations on manifolds. As corollaries we derive a Rabinowitz-type global bifurcation result and a Mawhin-type continuation principle. Finally, we deduce the existence of forced oscillations for the retarded spherical pendulum under general assumptions.File | Dimensione | Formato | |
---|---|---|---|
versione_finale_online.pdf
Accesso chiuso
Descrizione: Articolo principale
Tipologia:
Pdf editoriale (Version of record)
Licenza:
Tutti i diritti riservati
Dimensione
1.02 MB
Formato
Adobe PDF
|
1.02 MB | Adobe PDF | Richiedi una copia |
BeCaFuPe-JFPTA.pdf
Accesso chiuso
Descrizione: Articolo principale
Tipologia:
Altro
Licenza:
Tutti i diritti riservati
Dimensione
360.88 kB
Formato
Adobe PDF
|
360.88 kB | Adobe PDF | Richiedi una copia |
I documenti in FLORE sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.