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.