FUNCTIONAL DIFFERENTIAL EQUATIONS AND HENSTOCK-KURZWEIL INTEGRATION

Abstract

Retarded Functional Differential Equations are a natural generalisation of Ordiuary Differential Equations, This is understandable, as in reality most phenomena depend not only on the conditions of the present state but on its past history as well. The use of Riemann and Lebesgue integrals to study Functional Differential Equatious have proved useful, as illustrated in the studies by J. Hale. In this thesis we shall use Heustock-Kurzweil integration to study Functional Differeutial Equations. As it is well-known, Heustock-Kurzweil integral encompasses Riemann and Lebesgue integrals and also it has proved to be useful in the study of Ordinary Differential Equations and even Retarded Functional Differentail Equations with finite delay.