A Result of Ambrosetti-Prodi Type for First Order ODE's with Concave and Coercive Right Member

Abstract

In a family of periodic ordinary differential equations with concave and coercive right member, we obtain that the set of equations with an unique periodic solution is a submanifold of codimension one. We also show that the intersection of that set with an invariant by $\mathbb{R}$ affine manifold is the graph of a continuous function.