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.
2015
16
273
300
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Benevieri, Pierluigi; Calamai, Alessandro; Furi, Massimo; Pera, Maria Patrizia
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Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/898920
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