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On an a-bifurcation theorem with application to a parameterized integro-differential system

Authors: 

Nguyen Van Loi, Zhenhai Liu and Valeri Obukhovskii

Source title: 
Fixed Point Theory, 16(1): 127-142, 2015 (ISI)
Academic year of acceptance: 
2014-2015
Abstract: 

In this paper, we define a notion of an A-bifurcation for a system of differential equations in a separable Hilbert space. By using the methods of the topological degree theory and guiding functions, we prove the theorem on the existence and uniqueness of an A-bifurcation point. It is shown how the abstract result can be applied to study the global structure of the solution set of a feedback control system governed by integro-differential equations