BOUNDARY-VALUE PROBLEM WITH MIXED CONDITIONS FOR WEAKLY NONLINEAR HYPERBOLIC EQUATIONS

摘要

In a cylindrical domain, we investigate the unique solvability of a problem with mixed boundary conditions for an inhomogeneous linear hyperbolic equation of higher order with coefficients variable with respect to space coordinates. To estimate from below the small denominators that appear in the construction of a solution of the problem, the metric approach is used. The obtained results are extended to the case where the equation is perturbed by a nonlinear summand.