AN INFINITE DIMENSIONAL BIFURCATION PROBLEM WITH APPLICATION TO A CLASS OF FUNCTIONAL DIFFERENTIAL EQUATIONS OF NEUTRAL TYPE

摘要

In this paper we consider an infinite dimensional bifurcation equation depending on a parameter ε > 0. By means of the theory of condensing operators, we prove the existence of a branch of solutions, parametrized by e, bifurcating from a curve of solutions of the bifurcation equation obtained for ε = 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.