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Stability theorems for some functional equations. (English) Zbl 0274.45012

MSC:
45N05 Abstract integral equations, integral equations in abstract spaces
45D05 Volterra integral equations
45J05 Integro-ordinary differential equations
34K20 Stability theory of functional-differential equations
34G99 Differential equations in abstract spaces
34D20 Stability of solutions to ordinary differential equations
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References:
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[2] Avner Friedman, Partial differential equations of parabolic type, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1964. · Zbl 0092.31002
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[4] A. Halanay, On the asymptotic behavior of the solutions of an integro-differential equation, J. Math. Anal. Appl 10 (1965), 319 – 324. · Zbl 0136.10202 · doi:10.1016/0022-247X(65)90126-5 · doi.org
[5] Kenneth B. Hannsgen, Indirect abelian theorems and a linear Volterra equation, Trans. Amer. Math. Soc. 142 (1969), 539 – 555. · Zbl 0185.35801
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[7] Einar Hille and Ralph S. Phillips, Functional analysis and semi-groups, American Mathematical Society Colloquium Publications, vol. 31, American Mathematical Society, Providence, R. I., 1957. rev. ed. · Zbl 0078.10004
[8] J. J. Levin, The asymptotic behavior of the solution of a Volterra equation, Proc. Amer. Math. Soc. 14 (1963), 534 – 541. · Zbl 0115.32403
[9] J. J. Levin and J. A. Nohel, Note on a nonlinear Volterra equation, Proc. Amer. Math. Soc. 14 (1963), 924 – 929. · Zbl 0151.16904
[10] J. J. Levin and J. A. Nohel, Perturbations of a nonlinear Volterra equation, Michigan Math. J. 12 (1965), 431 – 447. · Zbl 0139.29304
[11] Michel Loève, Probability theory, 2nd ed. The University Series in Higher Mathematics. D. Van Nostrand Co., Inc., Princeton, N. J.-Toronto-New York-London, 1960. · Zbl 0095.12201
[12] R. C. MacCamy, Exponential stability for a class of functional differential equations., Arch. Rational Mech. Anal. 40 (1970/1971), 120 – 138. · Zbl 0215.15601 · doi:10.1007/BF00250317 · doi.org
[13] Heinz König and Josef Meixner, Lineare Systeme und lineare Transformationen, Math. Nachr. 19 (1958), 265 – 322 (German). · Zbl 0089.09303 · doi:10.1002/mana.19580190122 · doi.org
[14] John A. Nohel, Qualitative behaviour of solutions of nonlinear Volterra equations, Stability problems of solutions of differential equations (Proc. NATO Advanced Study Inst., Padua, 1965) Edizioni ”Oderisi”, Gubbio, 1966, pp. 177 – 210.
[15] M. M. Vaĭnberg, Variational methods for the study of non-linear operators, GITTL, Moscow, 1956; English transl., Holden-Day, San Francisco, 1964. MR 19, 567; 31 #638.
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