Keywords
- Bounded Solution
- Volterra Integral Equation
- Volterra Equation
- Resolvent Operator
- Resolvent Equation
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Bibliography
Bronikowski, T. A., An integrodifferential system which occurs in reactor dynamics, Arch. Rational Mech. Anal. 37 (1970), 363–380.
Coddington, E. A. and Levinson N., Theory of Ordinary Differential Equations, McGraw Hill Book Co., Inc., 1955.
Corduneanu, C., Problème globaux dans la théorie des équations intégrals de Volterra, Ann.Math. Pura Appl. 67 (1965), 349–363.
Grossman, S. I and Miller R. K., Perturbation theory for Volterra integrodifferential systems, J. Diff. Eq. 8 (1970), 457–474.
Grossman, S. I. and Miller, R. K., Nonlinear Volterra integrodifferential systems with L' kernels, (to appear).
Hannsgen, K. B., Indirect abelian theorems and a linear Volterra equation, Trans. Amer. Math. Soc. 142 (1969), 539–555.
Hannsgen, K. B., On a nonlinear Volterra equation, Mich. Math. J. 16 (1969), 365–376.
Kaplan, J. L., On the asymptotic behavior of Volterra integral equations, J. Math. Anal. Appl.
Levin, J. J., A nonlinear Volterra equation, not of convolution type, J. Differential Eq. 4 (1968), 176–186.
Levin, J. J. and Nohel, J. A., A system of integrodifferential equations occuring in reactor dynamics, J. Math. Mech. 9 (1960), 347–368.
Levin, J. J. and Nohel, J. A., Perturbations of a nonlinear Volterra equation, Mich. Math. J. 12 (1965) 431–446.
Levin, J. J. and Shea, D. F., On the asymptotic behavior of the bounded solutions of some integral equations, I, II, III, J. Math. Anal. Appl. (to appear).
MacCamy, R. C. and Wong, J. S. W., Stability theorems for some functional differential equations, Trans, AMS (to appear).
Massera, J. L., On Liapunov's conditions for stability, Ann. Math. 50 (1949), 705–721.
Massera, J. L. and Schäffer J. J., Linear Differential Equations and Function Spaces, Academic Press, N.Y. & London, 1966.
Miller, R. K., On the linearization of Volterra integral equations, J. Math. Anal. Appl. 23 (1968), 198–208.
Miller, R. K., On Volterra integral equations with nonnegative integrable resolvents, J. Math. Anal. Appl. 22 (1968), 319–340.
Miller, R. K., Admissibility and nonlinear Volterra integral equations, Proc. Amer. Math. Soc. 25 (1970), 45–71.
Miller, R. K., Asymptotic stability properties of linear Volterra integrodifferential equations, J. Differential Equations (to appear).
Miller, R. K., Nohel, J. A., and Wong, J. S. W., Perturbations of Volterra integral equations, J. Math. Anal. Appl. 25 (1969), 676–691.
Nohel, J. A., Remarks on nonlinear Volterra equations, Proc. U.S.-Japan Seminar Differential and Functional Equations, W. A. Benjamin, Inc., 1967, pp. 249–266.
Nohel, J. A., Asymptotic relationships between systems of Volterra equations, Annali di Mat. Pura ed Applic. (to appear).
Paley, R. E. A. C. and Wiener, N., Fourier Transforms in the Complex Domain, Amer. Math. Soc., Providence 1934.
Strauss, A., On a perturbed Volterra integral equation, J. Math. Anal. Appl. 30 (1970), 564–575.
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Nohel, J.A. (1971). Perturbations of volterra equations and admissibility. In: Urabe, M. (eds) Japan-United States Seminar on Ordinary Differential and Functional Equations. Lecture Notes in Mathematics, vol 243. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0058717
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DOI: https://doi.org/10.1007/BFb0058717
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