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Semilinear integrodifferential equations with nonlocal Cauchy problem. (English) Zbl 0916.45014

MSC:
 45N05 Abstract integral equations, integral equations in abstract spaces 45G10 Other nonlinear integral equations 45J05 Integro-ordinary differential equations
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References:
 [1] Pazy, A., Semigroups of linear operators and applications to partial differential equations, (1983), Springer Paris · Zbl 0516.47023 [2] Byszewski, L., Theorems about the existence and uniqueness of solutions of a semilinear evolution nonlocal Cauchy problem, J. math. analysis applic., 162, 494-505, (1991) · Zbl 0748.34040 [3] Byszewski, L.; Lakshmikantham, V., Theorem about the existence and uniqueness of a solution of a nonlocal abstract Cauchy problem in a Banach space, Applic. analysis, 40, 11-19, (1990) · Zbl 0694.34001 [4] Jackson, D., Existence and uniqueness of solutions to semilinear nonlocal parabolic equations, J. math. analysis applic., 172, 256-265, (1993) · Zbl 0814.35060 [5] Gripenberg, G.; Londen, S.-O.; Staffans, O., (), 12-13 [6] Grimmer, R., Resolvent operators for integral equations in a Banach space, Trans. am. math. soc., 273, 333-349, (1982) · Zbl 0493.45015 [7] Grimmer, R.; Liu, J., Liapunov — Razumikhin methods for integrodifferential equations in hubert space, (), 9-24 · Zbl 0818.45003 [8] Liu J., Resolvent operators and weak solutions of integrodifferential equations, Diff. Integral Eqns, to appear. [9] Burton, T., Stability and periodic solutions of ordinary differential equations and functional differential equations, (1985), Academic Press London · Zbl 0635.34001 [10] Bainov, D.; Simeonov, P., (), 1-2
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