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

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  • 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.


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