References
G. Prouse, “Soluzioni quasi-periodiche dell'equazione non omogenea delle onde, con termine dissipativo non lineare. I-IV,” Atti Accad. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8),38, No. 6, 804–807;39, No. 1–2, 11–18;39, No. 3–4, 155–160,39, No. 5, 240–244 (1965).
L. Amerio and G. Prouse, Almost-Periodic Functions and Functional Equations, Van Nostrand, New York (1971).
M. Biroli and A. Haraux, “Asymptotic behavior for an almost periodic, strongly dissipative wave equation,” J. Differential Equations,38, No. 3, 422–440 (1980).
A. Haraux, “Semilinear hyperbolic problems in bounded domains,” Math. Reports,3, Part 1, Harwood Academic Publishers, Gordon and Breach, New York (1987).
A. Haraux, “Nonresonance for a strongly dissipative wave equation in higher dimensions,” Manuscripta Math.,53, No. 1–2, 145–166 (1985).
M. Nakao, “Bounded, periodic or almost-periodic solutions of nonlinear hyperbolic partial differential equations,” J. Differential Equations,23, No. 3, 368–386 (1977).
M. Nakao, “Bounded, periodic and almost periodic classical solutions of some nonlinear wave equations with a dissipative term,” J. Math. Soc. Japan,30, No. 3, 375–394 (1978).
P. Marcati, “Almost-periodic solutions for a semilinear quasi-autonomous hyperbolic problem,” Nonlinear Anal.,10, No. 10, 1053–1067 (1986).
B. M. Levitan and V. V. Zhikov, Almost Periodic Functions and Differential Equations, Cambridge Univ. Press, Cambridge (1982).
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Translated from Matematicheskie Zametki, Vol. 54, No. 6, pp. 146–148, December, 1993.
The author is grateful to M. I. Vishik for the formulation of the problem and for his interest in the paper.
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Shirikyan, A.R. On classical almost-periodic solutions of nonlinear hyperbolic equations. Math Notes 54, 1288–1290 (1993). https://doi.org/10.1007/BF01209094
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DOI: https://doi.org/10.1007/BF01209094