Generic results for the existence of nondegenerate periodic solutions of some differential systems with periodic nonlinearities (Q1176505)

Let \(C^ 0_ T\) be the space of continuous \(T\)-periodic functions with the supremum norm. The main result in this paper provides conditions under which all the solutions of the \(N\)-dimensional differential system \(Lx+\nabla V(x)=y\) are nondegenerate when \(y\) belongs to a dense subset \({\mathcal G}\) of the set \(y\in C^ 0_ T\) with mean value zero. In this equation, \(L\) is a linear differential operator acting on \(T\)-periodic functions and \(V\) is a smooth function sublinear at infinity which satisfies a periodicity condition.