×

zbMATH — the first resource for mathematics

Existence and uniqueness of periodic solutions of linear differential equations in Banach spaces. (English) Zbl 0522.34055
MSC:
34G10 Linear differential equations in abstract spaces
34C25 Periodic solutions to ordinary differential equations
34A30 Linear ordinary differential equations and systems
PDF BibTeX XML Cite
Full Text: EuDML
References:
[1] Carroll R.: Systems of abstract differential equations in general spaces. Ricerche di Matematica, vol. XXVII, (1978), Fasc. 2^\circ . · Zbl 0398.35088
[2] Dezin A. A.: Operators with the first derivative and non-local boundary conditions. (Russian) Izv. AN SSSR Ser. mat. 31, (1967), 61-86.
[3] Donaldson J. A.: The abstract Cauchy problem. J. Dif. Eq. 25, (1977), 400-409. · Zbl 0326.35007
[4] Dubinskij Ju. A.: Periodic solutions of elliptico-parabolic equations. (Russian) Mat. sbornik, T. 76 (118), (1968), No. 4. · Zbl 0183.10903
[5] Dubinskij Ju. A.: On some differential-operator equations of a general type. (Russian) DAN SSSR, T. 201, (1971), No. 5.
[6] Dubinskij Ju. A.: On some differential-operator equations of an arbitrary order. (Russian) Mat. sbornik, 90 (132), (1973), No. 1.
[7] Geľfand I. M., Šilov G. E.: Generalized functions, vol. 1 - 3. (Russian) Moscow 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. · Zbl 0445.35013
[9] Hersh R.: Explicit solution of a class of higher-order abstract Cauchy problems. J. Dif. Eq. 8, (1970), 570-579. · Zbl 0208.38603
[10] Hille E., Phillips R. S.: Functional analysis and semigroups. AMS Colloquium publications volume XXXI, Providence 1957. · Zbl 0078.10004
[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. · Zbl 0226.35009
[12] Lions J. L.: Equations differentielles-operationelles et problèmes aux limites. Springer Berlin 1961, 50-51.
[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
[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
[15] da Prato G.: Weak solutions for linear abstract differential equations. Advances in Math. 5, (1970), No. 2. · Zbl 0244.34048
[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
[17] Sova M.: Periodic solutions of abstract evolution equations. Unpublished manuscript lectured in Novosibirsk in 1965.
[18] Sova M.: Solutions périodiques des équations différentielles operationelles: la méthode de développements de Fourier. Čas. pro pěst. mat. 93 (1968), 386-421. · Zbl 0179.20601
[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.
[20] Straškraba I., Vejvoda O.: Periodic solutions to a singular abstract differential equation. Czech. Math. J. 24 (99), (1974), 528-540. · Zbl 0329.34053
[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. · Zbl 0146.12904
[22] Vejvoda O., al.: Partial differential equations: Periodic solutions. Sijthoff Noordhoff 1981, Alphen aan den Rijn.
[23] Yosida K.: Functional Analysis. Springer-Verlag Berlin, Heidelberg, New York 1971. · Zbl 0217.16001
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.