Acta Mathematica Sinica, English Series

, Volume 23, Issue 6, pp 983–988

Existence of Semilinear Differential Equations with Nonlocal Initial Conditions

ORIGINAL ARTICLES

DOI: 10.1007/s10114-005-0839-3

Cite this article as:
Xue, X.M. Acta Math Sinica (2007) 23: 983. doi:10.1007/s10114-005-0839-3

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) + u0 when the map g loses compactness in Banach spaces.

Keywords

nonlocal conditioncompact semigroupmild solution

MR (2000) Subject Classification

34G1034G2047D06

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  1. 1.Department of MathematicsSoutheast UniversityNanjing 210096P. R. China