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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 ε, 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. [ABSTRACT FROM AUTHOR]

We consider a system of two semilinear parabolic inclusions depending on a small parameter ϵ>0 which is present both in front of the derivative in one of the two inclusions and in the nonlinear terms to model high-frequency inputs.The aim is to provide conditions in order to guarantee, for ϵ>0 sufficiently small, the existence of periodic solutions and in order to study their behaviour as ϵ tends to zero. Our assumptions permit the definition of upper semicontinuous, convex valued, compact vector operators whose fixed points represent the sought-after periodic solutions. The existence of fixed points is shown by using topological degree theory arguments. [Copyright &y& Elsevier]