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Perturbation theory for Volterra integrodifferential systems. (English) Zbl 0209.14101


MSC:

45J05 Integro-ordinary differential equations
45D05 Volterra integral equations
45M05 Asymptotics of solutions to integral equations
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References:

[1] Miller, R. K., On the linearization of Volterra integral equations, J. Math. Anal. Appl., 23, 198-208 (1968) · Zbl 0167.40902
[2] Miller, R. K.; Nohel, J. A.; Wong, J. S.W, Perturbations of integral equations, J. Math. Anal. Appl., 24 (1969) · Zbl 0185.35901
[3] Grossman, S. I., Existence and uniqueness of solutions to nonlinear Volterra integral and integrodifferential equations, (Ph.D. Thesis (1969), Brown University) · Zbl 0206.41402
[4] Banks, H. T., Representations for solutions of linear FDE’s, (Tech. Report (1968), Center for Dynamical Systems, Brown University: Center for Dynamical Systems, Brown University Providence, R. I) · Zbl 0165.42701
[5] Massera, J. L.; Schaffer, J. J., Linear Differential Equations and Function Spaces (1966), Academic Press: Academic Press New York · Zbl 0202.14701
[6] Corduneanu, C., Problèmes globaux dans la théorie des équations intégrales de Volterra, Ann. Mat. Pura Appl., 67, 349-363 (1965) · Zbl 0151.16801
[7] Corduneanu, C., Some perturbation problems in the theory of integral equations, Math. Systems Theory, 1, 143-155 (1967) · Zbl 0166.09801
[8] Antosiewicz, H. A., Un. Analogue du principle de point fixe de Banach, Ann. Math. Pura Appl., 74, 61-64 (1966) · Zbl 0151.20602
[9] Levin, J. J.; Nohel, J. A., On a system of integrodifferential equations occuring in reactor dynamics, J. Math. Mech., 9, 347-368 (1960) · Zbl 0094.08503
[10] Gyftopoulos, E. P., Theoretical and experimental criterion for nonlinear reactor stability, Nucl. Sci. Eng., 26, 26-33 (1966)
[11] Paley, R. E.A. C.; Wiener, N., Fourier Transforms in the Complex Domain (1934), Amer. Math. Soc. Colloquium Publications · Zbl 0006.25704
[12] Helliwell, W. S., The asymptotic behavior of the solution to a nonlinear system of integrodifferential equations occurring in reactor dynamics, (Ph.D. Thesis (1969), Brown University)
[13] Levin, J. J., The asymptotic behavior of the solutions of an integrodifferential equation, (Proc. Amer. Math. Soc., 14 (1963)), 534-541 · Zbl 0115.32403
[14] Hannsgen, K. B., Indirect Abelian theorems and a linear Volterra equation, Trans. Amer. Math. Soc., 142, 539-555 (1969) · Zbl 0185.35801
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