We consider T-periodic parametrized retarded functional differential equations, with infinite delay, on (possibly) noncompact manifolds. Using a topological approach, based on the notions of degree of a tangent vector field and of the fixed point index, we prove a global continuation result for T-periodic solutions of such equations. Our main theorem is a generalization to the case of retarded equations of a global continuation result obtained by the last two authors for ordinary differential equations on manifolds. As corollaries we obtain a Rabinowitz type global bifurcation result and a continuation principle of Mawhin type.

Global continuation of periodic solutions for retarded functional differential equations on manifolds / P. Benevieri; A. Calamai; M. Furi; M.P. Pera. - In: BOUNDARY VALUE PROBLEMS. - ISSN 1687-2770. - ELETTRONICO. - 2013:21:(2013), pp. 1-19. [10.1186/1687-2770-2013-21]

Global continuation of periodic solutions for retarded functional differential equations on manifolds

BENEVIERI, PIERLUIGI;FURI, MASSIMO;PERA, MARIA PATRIZIA
2013

Abstract

We consider T-periodic parametrized retarded functional differential equations, with infinite delay, on (possibly) noncompact manifolds. Using a topological approach, based on the notions of degree of a tangent vector field and of the fixed point index, we prove a global continuation result for T-periodic solutions of such equations. Our main theorem is a generalization to the case of retarded equations of a global continuation result obtained by the last two authors for ordinary differential equations on manifolds. As corollaries we obtain a Rabinowitz type global bifurcation result and a continuation principle of Mawhin type.
2013
2013:21
1
19
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P. Benevieri; A. Calamai; M. Furi; M.P. Pera
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Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/787926
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