, Volume 23, Issue 6, pp 983-988
Date: 14 Sep 2006

Existence of Semilinear Differential Equations with Nonlocal Initial Conditions

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Abstract

In this paper we give the existence of mild solutions for semilinear Cauchy problems u'(t) = Au(t) + f(t, u(t)), t ∈¸ I, a.e. with nonlocal initial condition u(0) = g(u) + u 0 when the map g loses compactness in Banach spaces.