An infinite dimensional bifurcation problem with application to a class of functional differential equations of neutral type

In this paper we consider an infinite dimensional bifurcation equation depending on a parameter epsilon > 0. By means of the theory of condensing operators, we prove the existence of a branch of solutions, parametrized by epsilon, bifurcating from a curve of solutions of the bifurcation equation obtained for epsilon = 0. We apply this result to a specific problem, namely to the existence of periodic solutions bifurcating from the limit cycle of an autonomous functional differential equation of neutral type when it is periodically perturbed by a nonlinear perturbation term of small amplitude.