Linear periodic boundary-value problem for a second-order hyperbolic equation. II. Quasilinear problem
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.
English version (Springer): Ukrainian Mathematical Journal 50 (1998), no. 12, pp 1917-1923.
Citation Example: Khoma N. H. Linear periodic boundary-value problem for a second-order hyperbolic equation. II. Quasilinear problem // Ukr. Mat. Zh. - 1998. - 50, № 12. - pp. 1680–1685.