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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.

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  1. Department of Mathematics, Southeast University, Nanjing 210096, P. R. China

    Xing Mei Xue

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  1. Xing Mei Xue
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Xue, X.M. Existence of Semilinear Differential Equations with Nonlocal Initial Conditions. Acta Math Sinica 23, 983–988 (2007). https://doi.org/10.1007/s10114-005-0839-3

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  • DOI: https://doi.org/10.1007/s10114-005-0839-3

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