Abstract
We investigate the linear periodic problem u tt −u xx =F(x, t), u(x+2π, t)=u(x, t+T)=u(x, t), ∈ ℝ2, and establish conditions for the existence of its classical solution in spaces that are subspaces of the Vejvoda-Shtedry spaces.
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References
Yu. A. Mitropol’skii, G. P. Khoma, and M. I. Gromyak, Asymptotic Methods for Investigation of Quasiwave Equations of Hyperbolic Type [in Russian], Naukova Dumka, Kiev (1991).
O. Vejvoda and M. Shtedry, “The existence of classical periodic solutions of a wave equation: The relation of the number-theoretic character of the period with geometric properties of solutions,” Differents. Uravn., 20, No. 10, 1733–1739 (1984).
Additional information
Ternopol’ Pedagogical Institute, Ternopol’. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 2, pp. 302–308, February, 1997.
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Khoma, L.G., Khoma, N.G. & Botyuk, A.O. Existence of the Vejvoda-Shtedry spaces. Ukr Math J 49, 334–341 (1997). https://doi.org/10.1007/BF02486447
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DOI: https://doi.org/10.1007/BF02486447