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
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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
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