Boundary-Value Problem for Weakly Nonlinear Hyperbolic Equations with Variable Coefficients - Bilusyak, N.I.; Ptashnik, B. I. (Ukrains’kyi Matematychnyi Zhurnal, 2001)
We establish conditions for the unique solvability of a boundary-value problem for a weakly nonlinear hyperbolic equation of order 2n, n > (3p + 1)/2, with coefficients dependent on the space coordinates and data given on the entire boundary of a cylindric domain \(D \subset \mathbb{R}^{p + 1}\) . The investigation of this problem is connected with the problem of small denominators.