The regularity of almost-periodic differential operators of neutral type appearing in the averaging principle. (English. Russian original) Zbl 0357.34038
Ukr. Math. J. 28(1976), 513-518 (1977); translation from Ukr. Mat. Zh. 28, 663-670 (1976).
MSC:
| 34C30 | Manifolds of solutions of ODE (MSC2000) |
| 47E05 | General theory of ordinary differential operators |
| 34C25 | Periodic solutions to ordinary differential equations |
References:
| [1] | M. A. Krasnosel’skii, V. Sh. Burd, and Yu. S. Kolesov, Nonlinear Almost-Periodic Vibrations [in Russian], Nauka, Moscow (1970). |
| [2] | V. Sh. Burd, ?The averaging principle on an infinite interval for functional differential equations, and almost-periodic vibrations of quasi-linear systems,? Vestnik Yaroslav. Univ.,7, 89-115 (1974). |
| [3] | É. Mukhamadiev, ?The invertibility of functional operators in the space of functions bounded on the real line,? Matem. Zametki,11, No. 3, 269-274 (1972). |
| [4] | B. M. Levitan, Almost-Periodic Functions [in Russianl, Gostekhizdat, Moscow (1953). · Zbl 1222.42002 |
| [5] | R. R. Akhmerov, ?On the averaging principle for functional differential equations of neutral type,? Ukr. Mat. Zh.,25, No. 5, 579-588 (1973). |
| [6] | B. N. Sadovskii, ?Limit compact and condensing operators,? Usp. Mat. Nauk,27, No. 1 (163), 81-146 (1972). · Zbl 0232.47067 |
| [7] | R. R. Akhmerov and M. I. Kamenskii, ?The averaging principle and the stability of periodic solutions of equations of neutral type,? Trudy Nauchno. Issled. Inst. Matem. Voronezh. Gos. Univ.,15, 9-13 (1974). |
| [8] | R. R. Akhmerov and M. I. Kamenskii, ?On an approach to an investigation of the stability of the periodic solutions in the averaging principle for functional differential equations of neutral type,? Comm. Math. Univ. Carolinae,16, No. 2, 293-313 (1975). |
| [9] | R. R. Akhmerov, ?The averaging principle and almost-periodic solutions of systems of functional differential equations of neutral type,? Differentsial’nye Uravneniya,11, No. 2, 211-221 (1975). |
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