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# 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 $\varepsilon>0 .$ By means of the theory of condensing operators, we prove the existence of a branch of solutions, parametrized by $\varepsilon ,$ bifurcating from a curve of solutions of the bifurcation equation obtained for $\varepsilon =0 .$ 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.
Mathematics Subject Classification: Primary: 47H08, 34K18, 34K40; Secondary: 34K13, 34K27.

 Citation:

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