UNIFIED TREATMENT OF LOCAL THEORY OF NFDES WITH INFINITE DELAY
Keywords:local theory, unbounded delay equations, local unbounded delay equations
The present paper gives a unified treatment of the local theory of NFDEs with infinite delay on a class of comparatively comprehensive phase spaces which contain admissible phase spaces and BC space as special cases. Condi- tions and assumptions are imposed on two functionals defining the equation, and therefore independent of the structure and properties of phase spaces. This al- lows us to determine phase spaces and sufficient conditions guaranteeing existence and uniqueness of solutions according to the property of the equation at hand as opposed to preassign a phase space to dictate the conditions. An example will be given to show how to choose the phase space according to the fading memory characteristic of Volterra integrodifferential equations so that the Cauchy initial value problem is well posed.
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