We apply the topological tools of fixed point index and of degree of a tangent vector field to the study of the set of harmonic solutions to periodic perturbations of autonomous ODEs on (smooth) boundaryless differentiable manifolds, allowing the perturbation to contain a distributed, possibly infinite, delay. In order to do so, we construct a Poincare'-type T-translation operator on an appropriate function space and, in the unperturbed case, prove a formula for its fixed point index in terms of the degree of the autonomous vector field.

Periodic solutions of retarded functional perturbations of autonomous differential equations on manifolds / M. Furi; M.P. Pera; M. Spadini. - In: COMMUNICATIONS IN APPLIED ANALYSIS. - ISSN 1083-2564. - STAMPA. - 15:(2011), pp. 381-394.

Periodic solutions of retarded functional perturbations of autonomous differential equations on manifolds

FURI, MASSIMO;PERA, MARIA PATRIZIA;SPADINI, MARCO
2011

Abstract

We apply the topological tools of fixed point index and of degree of a tangent vector field to the study of the set of harmonic solutions to periodic perturbations of autonomous ODEs on (smooth) boundaryless differentiable manifolds, allowing the perturbation to contain a distributed, possibly infinite, delay. In order to do so, we construct a Poincare'-type T-translation operator on an appropriate function space and, in the unperturbed case, prove a formula for its fixed point index in terms of the degree of the autonomous vector field.
2011
15
381
394
M. Furi; M.P. Pera; M. Spadini
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Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/543284
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