Calculus of Variations and Geometric Measure Theory

Incontri di Analisi Matematica tra Firenze, Pisa e Siena

Existence and global bifurcation of periodic solutions for retarded functional differential equations on manifolds

Patrizia Pera

created by paolini on 30 Apr 2019

17 may 2019 -- 15:20   [open in google calendar]

Abstract.

In this talk, I will present some results on the existence and global bifurcation of periodic solutions to first and second order retarded functional differential equations on boundaryless smooth manifolds. I will consider both cases of a topologically nontrivial compact manifold (e.g., an even dimensional sphere) and of a possibly noncompact constraint, assuming in the latter case that the topological degree of a suitable tangent vector field is nonzero. The approach is topological and based on the fixed point index theory for locally compact maps on metric Absolute Neighborhood Retracts (ANRs). Finally, I will show how to deduce from our results a Rabinowitz-type global bifurcation result as well as a Mawhin-type continuation principle.