Abstract
We investigate 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 is 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.
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To the outstanding mathematician Andrzej Granas whose contribution to the fixed point index theory made the existence of this article possible
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Benevieri, P., Calamai, A., Furi, M. et al. Global continuation of forced oscillations of retarded motion equations on manifolds. J. Fixed Point Theory Appl. 16, 273–300 (2014). https://doi.org/10.1007/s11784-015-0215-6
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DOI: https://doi.org/10.1007/s11784-015-0215-6