Applications of topological degree theory to some differential equations with singularities

P. AMSTER

Conferencia; Seminario de Ecuaciones Diferenciales No Lineales; 2015

We prove existence and multiplicity of periodic motions for somesingular problems using topological degree. More precisely, we shallassume there is a central force (attractive or repulsive) and an external force λh(t), periodic in time. The periodic second primitive of h(t) defines a planar curve and the number of periodic solutions of the differential equation islinked to the number of loops of this curve, at least when theparameter λ is large.