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.File | Dimensione | Formato | |
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