Approximation methods and the generalised Fuller index for semi-flows in Banach spaces

Abstract

In [3] Fuller introduced an index (now called the Fuller index) in order to study periodic solutions of ordinary differential equations. The objective of this paper is to give a simple generalisation of the Fuller index which can be used to study periodic points of flows in Banach spaces. We do not claim any significant breakthrough but merely suggest that the simplistic approach, presented here, might prove useful for the study of non-linear differential equations. We show our results can be used to study functional differential equations.