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.

Couchouron, J._.F., M., K., & Nistri, P. (2013). An infinite dimensional bifurcation problem with application to a class of functional differential equations of neutral type. COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 12(5), 1845-1859 [10.3934/cpaa.2013.12].

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

NISTRI, PAOLO
2013

Abstract

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.
Couchouron, J._.F., M., K., & Nistri, P. (2013). An infinite dimensional bifurcation problem with application to a class of functional differential equations of neutral type. COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 12(5), 1845-1859 [10.3934/cpaa.2013.12].
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11365/7033
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