Xue, Xing Mei, Existence of Semilinear Differential Equations with Nonlocal Initial Conditions, Acta mathematica Sinica. English series (Print) , 23(6), 2007, pp. 983-988
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