In this paper, we show existence and uniqueness of a solution to a functional differential equation with infinite delay. We choose an appropriate Frechet space so as to cover a large class of functions to be used as initial functions to obtain existence and uniqueness of solutions.
A theorem on asymptotic stability is obtained for a differential equation with an infinite delay in a function space which is suitable for the numerical computation of the solution to the infinite delay equation.
Abstract. In this paper, a Banach phase space containing BC(−∞, 0] and contained in C(−∞, 0] is defined with which existence of a solution and convergence of a discrete scheme are proved for an infinite delay differential equation.
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