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Non-autonomous integrodifferential equations with non-local conditions. (English) Zbl 1044.45002
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.

45N05Abstract integral equations, integral equations in abstract spaces
45J05Integro-ordinary differential equations
45G10Nonsingular nonlinear integral equations
Full Text: DOI
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[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
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[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