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

作者：Couchouron Jean Francois^*; Kamenskii Mikhail; Nistri Paolo

来源：Communications on Pure and Applied Analysis, 2013, 12(5): 1845-1859.

DOI：10.3934/cpaa.2013.12.1845

• Condensing operators
• bifurcation
• functional differential equations
• periodic solutions

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.

• 出版日期2013-9