This is a preview of subscription content, log in via an institution to check access.
Literature Cited
Yu. L. Daletskii (Ju. L. Daleckii) and M. G. Krein, Stability of Solutions of Differential Equations in Banach Space, Amer. Math. Soc., Providence (1974).
M. Amerio and G. Prouse, Almost-Periodic Functions and Functional Equations, Van Nostrand Reinhold, New York (1971).
H. Bart, “Periodic strongly continuous semigroups,” Ann. Mat. Pura Appl.,115, 311–318 (1977).
H. Bart and S. Goldberg, “Characterizations of almost-periodic strongly continuous groups and semigroups,” Math. Ann.,236, 105–116 (1978).
H. O. Fattorini, “Uniformly bounded cosine functions in Hilbert space,” Indiana Univ. Math. J.,20, 411–425 (1970).
E. Giusti, “Funzione coseno periodiche,” Boll. Un. Mat. Ital.,22, No. 4, 478–485 (1967).
Yu. I. Lyubich, “Almost-periodic functions in the spectral analysis of operators,” Dokl. Akad. Nauk SSSR,132, No. 3, 518–520 (1960).
Yu. I. Lyubich, “On completeness conditions for a system of eigenvectors of a correct operator,” Usp. Mat. Nauk,18, No. 1 (109), 165–171 (1963).
G. Vainikko, Analysis of Discretization Methods [in Russian], Tartu (1976).
G. M. Vainikko and S. I. Piskarev, “Regularly consistent operators,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 10, 25–36 (1977).
A. A. Samarskii and A. V. Gulin, “On certain results and problems in the stability theory of difference schemes,” Mat. Sb.,99, (141), No. 3, 299–330 (1976).
H. O. Fattorini, “Ordinary differential equations in linear topological space. II,” J. Diff. Equations,6, No. 1, 50–70 (1969).
A. V. Gulin, “Stability criteria for certain non-self-adjoint three-layer difference schemes,” Differents. Uravn.,16, No. 7, 1205–1210 (1980).
M. Sova, “Cosine operator functions,” Rozprawy Mat.,49, 3–46 (1966).
B. Nagy, “On cosine operator functions in Banach spaces,” Acta Sci. Math.,36, Nos. 3–4, 281–289 (1974).
S. I. Piskarev, “The discretization of an abstract hyperbolic equation,” Uch. Zap. Tartusk. Univ.,500, 3–23.
S. I. Piskarev, “On the compact convergence of the resolvent and semigroups,” in: Materials of the Conference “Methods of Algebra and Functional Analysis for the Study of Families of Operators,” Tartu (1978), pp. 71–74.
A. A. Samarskii and E. S. Nikolaev, Methods of Solving Finite-Difference Equations [in Russian], Nauka, Moscow (1978).
E. Hille and R. S. Phillips, Functional Analysis and Semigroups, Amer. Math. Soc., Providence (1957).
J. A. Goldstein, C. Radon, and R. E. Showalter, “Convergence rate of ergodic limits for semigroups and cosine functions,” Semigroup Forum,12, 189–206 (1976).
B. Nagy, “On cosine operator functions,” Publ. Math.,26, Nos. 3–4, 133–138 (1979).
Additional information
Translated from Sibirskii Matematicheskii Zhurnal, Vol. 25, No. 3, pp. 137–147, May–June, 1984.
Rights and permissions
About this article
Cite this article
Piskarev, S.I. Almost-periodic solutions of second-order differential equations. Sib Math J 25, 451–460 (1984). https://doi.org/10.1007/BF00968986
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00968986