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

MSC:
45N05Abstract integral equations, integral equations in abstract spaces
45G10Nonsingular nonlinear integral equations
45J05Integro-ordinary differential equations
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Full Text: DOI
References:
[1] Pazy, A.: Semigroups of linear operators and applications to partial differential equations. (1983) · 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.: Volterra integral and functional equations. 12-13 (1990) · Zbl 0695.45002
[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. Delay and differential equations, 9-24 (1992) · 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) · Zbl 0635.34001
[10] Bainov, D.; Simeonov, P.: Integral inequalities and applications. 1-2 (1992)