| Title:
|
Existence and uniqueness of periodic solutions of linear differential equations in Banach spaces (English) |
| Author:
|
Straškraba, Ivan |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
32 |
| Issue:
|
1 |
| Year:
|
1982 |
| Pages:
|
53-76 |
| Summary lang:
|
Russian |
| . |
| Category:
|
math |
| . |
| MSC:
|
34C25 |
| MSC:
|
34G10 |
| MSC:
|
47D05 |
| idZBL:
|
Zbl 0522.34055 |
| idMR:
|
MR646712 |
| DOI:
|
10.21136/CMJ.1982.101784 |
| . |
| Date available:
|
2008-06-09T14:46:51Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/101784 |
| . |
| Reference:
|
[1] Carroll R.: Systems of abstract differential equations in general spaces.Ricerche di Matematica, vol. XXVII, (1978), Fasc. 2°. Zbl 0398.35088, MR 0527417 |
| Reference:
|
[2] Dezin A. A.: Operators with the first derivative and non-local boundary conditions.(Russian) Izv. AN SSSR Ser. mat. 31, (1967), 61-86. MR 0213762 |
| Reference:
|
[3] Donaldson J. A.: The abstract Cauchy problem.J. Dif. Eq. 25, (1977), 400-409. Zbl 0326.35007, MR 0454219, 10.1016/0022-0396(77)90053-5 |
| Reference:
|
[4] Dubinskij Ju. A.: Periodic solutions of elliptico-parabolic equations.(Russian) Mat. sbornik, T. 76 (118), (1968), No. 4. Zbl 0183.10903, MR 0233058 |
| Reference:
|
[5] Dubinskij Ju. A.: On some differential-operator equations of a general type.(Russian) DAN SSSR, T. 201, (1971), No. 5. |
| Reference:
|
[6] Dubinskij Ju. A.: On some differential-operator equations of an arbitrary order.(Russian) Mat. sbornik, 90 (132), (1973), No. 1. |
| Reference:
|
[7] Geľfand I. M., Šilov G. E.: Generalized functions, vol. 1 - 3.(Russian) Moscow 1958. |
| Reference:
|
[8] Herrmann L.: Periodic solutions of the abstract differential equations: Fourier method.(Czech.) Thesis 1977, Mathematical Institute of the Czechoslovak Academy of Sciences, Praha. |
| Reference:
|
[9] Hersh R.: Explicit solution of a class of higher-order abstract Cauchy problems.J. Dif. Eq. 8, (1970), 570-579. Zbl 0208.38603, MR 0270210 |
| Reference:
|
[10] Hille E., Phillips R. S.: Functional analysis and semigroups.AMS Colloquium publications volume XXXI, Providence 1957. Zbl 0078.10004 |
| Reference:
|
[11] Krylová N., Vejvoda O.: Periodic solutions to partial differential equations, especially to a biharmonic wave equation.Symposia Matematica 7, 85 - 96, Academic Press, New York-London, 1971. Zbl 0226.35009, MR 0336018 |
| Reference:
|
[12] Lions J. L.: Equations differentielles-operationelles et problèmes aux limites.Springer Berlin 1961, 50-51. MR 0153974 |
| Reference:
|
[13] Lions J. L., Magenes E.: Problèmes aux limites non homogènes et applications. Vol. 1.Dunod, Paris 1968, 279-282, Vol. 3, Dunod, Paris 1970, 171-174. Zbl 0165.10801, MR 0247243 |
| Reference:
|
[14] Lovicar V.: Almost periodicity of solutions of the equation $x'(t) = A(t) x(t)$ with unbounded commuting operators.Čas. pro pěst. mat., 100 (1975), 36-45. Zbl 0363.34041, MR 0415031 |
| Reference:
|
[15] da Prato G.: Weak solutions for linear abstract differential equations.Advances in Math. 5, (1970), No. 2. Zbl 0244.34048, 10.1016/0001-8708(70)90033-2 |
| Reference:
|
[16] Sobolevskij P. E., Pogorelenko V. A.: On periodic solutions of hyperbolic equations.(Russian.) Trudy V. Mežd. Konf. Nelin. Koleb., Tom 1, Inst. Mat. Akad. Nauk USSR, Kiev 1970, 530-534. Zbl 0224.35052 |
| Reference:
|
[17] Sova M.: Periodic solutions of abstract evolution equations.Unpublished manuscript lectured in Novosibirsk in 1965. |
| Reference:
|
[18] Sova M.: Solutions périodiques des équations différentielles operationelles: la méthode de développements de Fourier.Čas. pro pěst. mat. 93 (1968), 386-421. MR 0248434 |
| Reference:
|
[19] Straškraba I., Vejvoda O.: Periodic solutions to abstract differential equations.Czech. Math. J. 23 (98), (1973), 849-876; Correction: Czech. Math. J. 27 (102), (1977), 511-513. MR 0456912 |
| Reference:
|
[20] Straškraba I., Vejvoda O.: Periodic solutions to a singular abstract differential equation.Czech. Math. J. 24 (99), (1974), 528-540. |
| Reference:
|
[21] Taam C. T.: Stability, periodicity, and almost periodicity of the solutions of nonlinear differential equations in Banach spaces.J. Math. Mech. 15 (1966), 849-876. MR 0196241 |
| Reference:
|
[22] Vejvoda O., al.: Partial differential equations: Periodic solutions.Sijthoff Noordhoff 1981, Alphen aan den Rijn. |
| Reference:
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[23] Yosida K.: Functional Analysis.Springer-Verlag Веrlin, Heidelberg, New York 1971. Zbl 0217.16001 |
| . |
