Abstract
This chapter discusses the functional differential equations of neutral type. A neutral functional differential equation (NFDE) is a differential relation in which the derivative of the unknown function may depend on past values of the function and its derivative. In contrast to retarded equations, even the basic problem of existence, uniqueness, and continuous dependence does not have a straightforward solution. The manner in which the norm on the initial data depends on the derivative plays a significant role. There is a tremendous amount of work being done, especially in the USSR, on neutral equations with initial data that have derivatives whose pth power is integrable. However, a qualitative theory has not been developed. In 1967, a particular class of neutral equations was introduced for which initial data could be specified in the space of continuous functions. In subsequent years, this class was further restricted in such a way that a qualitative theory now seems possible.
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