Abstract
In three spaces, we find exact classical solutions of the boundary-value periodic problem utt - a2uxx = g(x, t) u(0, t) = u(π, t) = 0, u(x, t + T) = u(x, t), x ∈ ℝ, t ∈ ℝ. We study the periodic boundary-value problem for a quasilinear equation whose left-hand side is the d’Alembert operator and whose right-hand side is a nonlinear operator.
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L. G. Khoma and N. G. Khoma, “On the properties of solutions of one boundary-value problem,” Dop. Akad. Nauk Ukr., No. 3, 38–40 (1994).
N. G. Khoma, “Spaces of solutions of one boundary-value problem,” Dop. Akad. Nauk Ukr., No. 1, 30–32 (1996).
N. G. Khoma, “Linear periodic boundary-value problem for a second-order hyperbolic equation. I,” Ukr. Mat. Zh., 50, No. 11, 1537–1544 (1998).
Yu. A. Mitropol’skii and N. G. Khoma, “Periodic solutions of quasilinear hyperbolic equations of the second order,” Ukr. Mat. Zh., 47, No. 10, 1370–1375 (1995).
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 12, pp. 1680–1685, December, 1998.
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Khoma, N.G. Linear periodic boundary-value problem for a second-order hyperbolic equation. II. Quasilinear problem. Ukr Math J 50, 1917–1923 (1998). https://doi.org/10.1007/BF02514207
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DOI: https://doi.org/10.1007/BF02514207