Liu, James H.; Ezzinbi, Khalil Non-autonomous integrodifferential equations with non-local conditions. (English) Zbl 1044.45002 J. Integral Equations Appl. 15, No. 1, 79-93 (2003). The authors investigate the existence and uniqueness of mild and classical solutions for a non-autonomous semilinear integrodifferential equation with non-local Cauchy problems in Banach spaces. Reviewer: Hu Chuangan (Tianjin) Cited in 2 ReviewsCited in 13 Documents MSC: 45N05 Abstract integral equations, integral equations in abstract spaces 45J05 Integro-ordinary differential equations 45G10 Other nonlinear integral equations Keywords:non-local condition; non-autonomous semilinear integrodifferential equation; resolvent operators; mild solution; classical solution; non-local Cauchy problems; Banach spaces PDFBibTeX XMLCite \textit{J. H. Liu} and \textit{K. Ezzinbi}, J. Integral Equations Appl. 15, No. 1, 79--93 (2003; Zbl 1044.45002) Full Text: DOI References: [1] L. Byszewski, Theorems about the existence and uniqueness of solutions of a semilinear evolution nonlocal Cauchy problem , J. Math. Anal. Appl. 162 (1991), 494-505. · Zbl 0748.34040 · doi:10.1016/0022-247X(91)90164-U [2] L. Byszewski and V. Lakshmikantham, Theorem about the existence and uniqueness of a solution of a nonlocal abstract Cauchy problem in a Banach space , Applicable Anal. 40 (1990), 11-19. · Zbl 0694.34001 · doi:10.1080/00036819008839989 [3] R. Grimmer, Resolvent operators for integral equations in a Banach space , Trans. Amer. Math. Soc. 273 (1982), 333-349. · Zbl 0493.45015 · doi:10.2307/1999209 [4] G. Gripenberg, S-O. Londen and O. Staffans, Volterra integral and functional equations , Cambridge University Press, Cambridge, 1990, 12-13. · Zbl 0695.45002 [5] D. Jackson, Existence and uniqueness of solutions to semilinear nonlocal parabolic equations , J. Math. Anal. Appl. 172 (1993), 256-265. · Zbl 0814.35060 · doi:10.1006/jmaa.1993.1022 [6] Y. Lin, Analytical and numerical solutions for a class of non-local non-linear parabolic differential equations , SIAM J. Math. Anal. 25 (1994), 1577-1594. · Zbl 0807.35069 · doi:10.1137/S003614109324306X [7] Y. Lin and J. Liu, Semilinear integrodifferential equations with nonlocal Cauchy problem , J. Nonlinear Anal. 26 (1996), 1023-1033. · Zbl 0916.45014 · doi:10.1016/0362-546X(94)00141-0 [8] J. Liu, Integrodifferential equations with non autonomous operators , J. Dynamic Systems Appl. 7 (1998), 427-440. · Zbl 0928.45008 [9] A. Pazy, Semigroups of linear operators and applications to partial differential equations , Springer-Verlag, New York, 1983. · Zbl 0516.47023 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.