Existence and uniqueness of periodic solutions of linear differential equations in Banach spaces

Ivan Straškraba

Czechoslovak Mathematical Journal (1982)

  • Volume: 32, Issue: 1, page 53-76
  • ISSN: 0011-4642

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Straškraba, Ivan. "Existence and uniqueness of periodic solutions of linear differential equations in Banach spaces." Czechoslovak Mathematical Journal 32.1 (1982): 53-76. <http://eudml.org/doc/13295>.

@article{Straškraba1982,
author = {Straškraba, Ivan},
journal = {Czechoslovak Mathematical Journal},
keywords = {existence; uniqueness; periodic solutions; linear differential equations; complex Banach space},
language = {eng},
number = {1},
pages = {53-76},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Existence and uniqueness of periodic solutions of linear differential equations in Banach spaces},
url = {http://eudml.org/doc/13295},
volume = {32},
year = {1982},
}

TY - JOUR
AU - Straškraba, Ivan
TI - Existence and uniqueness of periodic solutions of linear differential equations in Banach spaces
JO - Czechoslovak Mathematical Journal
PY - 1982
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 32
IS - 1
SP - 53
EP - 76
LA - eng
KW - existence; uniqueness; periodic solutions; linear differential equations; complex Banach space
UR - http://eudml.org/doc/13295
ER -

References

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  1. Carroll R., Systems of abstract differential equations in general spaces, Ricerche di Matematica, vol. XXVII, (1978), Fasc. 2°. (1978) Zbl0398.35088MR0527417
  2. Dezin A. A., Operators with the first derivative and non-local boundary conditions, (Russian) Izv. AN SSSR Ser. mat. 31, (1967), 61-86. (1967) MR0213762
  3. Donaldson J. A., 10.1016/0022-0396(77)90053-5, J. Dif. Eq. 25, (1977), 400-409. (1977) Zbl0326.35007MR0454219DOI10.1016/0022-0396(77)90053-5
  4. Dubinskij Ju. A., Periodic solutions of elliptico-parabolic equations, (Russian) Mat. sbornik, T. 76 (118), (1968), No. 4. (1968) Zbl0183.10903MR0233058
  5. Dubinskij Ju. A., On some differential-operator equations of a general type, (Russian) DAN SSSR, T. 201, (1971), No. 5. (1971) 
  6. Dubinskij Ju. A., On some differential-operator equations of an arbitrary order, (Russian) Mat. sbornik, 90 (132), (1973), No. 1. (1973) 
  7. Geľfand I. M., Šilov G. E., Generalized functions, vol. 1 - 3, (Russian) Moscow 1958. (1958) 
  8. Herrmann L., Periodic solutions of the abstract differential equations: Fourier method, (Czech.) Thesis 1977, Mathematical Institute of the Czechoslovak Academy of Sciences, Praha. (1977) 
  9. Hersh R., Explicit solution of a class of higher-order abstract Cauchy problems, J. Dif. Eq. 8, (1970), 570-579. (1970) Zbl0208.38603MR0270210
  10. Hille E., Phillips R. S., Functional analysis and semigroups, AMS Colloquium publications volume XXXI, Providence 1957. (1957) Zbl0078.10004
  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. (1971) Zbl0226.35009MR0336018
  12. Lions J. L., Equations differentielles-operationelles et problèmes aux limites, Springer Berlin 1961, 50-51. (1961) Zbl0098.31101MR0153974
  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. (1968) Zbl0165.10801MR0247243
  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. (1975) Zbl0363.34041MR0415031
  15. da Prato G., 10.1016/0001-8708(70)90033-2, Advances in Math. 5, (1970), No. 2. (1970) Zbl0244.34048DOI10.1016/0001-8708(70)90033-2
  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. (1970) Zbl0224.35052
  17. Sova M., Periodic solutions of abstract evolution equations, Unpublished manuscript lectured in Novosibirsk in 1965. (1965) 
  18. Sova M., Solutions périodiques des équations différentielles operationelles: la méthode de développements de Fourier, Čas. pro pěst. mat. 93 (1968), 386-421. (1968) Zbl0179.20601MR0248434
  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. (1973) Zbl0275.34063MR0456912
  20. Straškraba I., Vejvoda O., Periodic solutions to a singular abstract differential equation, Czech. Math. J. 24 (99), (1974), 528-540. (1974) Zbl0329.34053
  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. (1966) Zbl0146.12904MR0196241
  22. Vejvoda O., al., Partial differential equations: Periodic solutions, Sijthoff Noordhoff 1981, Alphen aan den Rijn. (1981) Zbl0183.10401
  23. Yosida K., Functional Analysis, Springer-Verlag Веrlin, Heidelberg, New York 1971. (1971) Zbl0217.16001

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