Boundary-Value Problem for Weakly Nonlinear Hyperbolic Equations with Variable Coefficients

Abstract

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.