The smoothness of solutions of the problems with nonlocal multi-point conditions for strictly hyperbolic equations

Abstract

We consider the problem with nonlocal multi-point boundary conditions for high order in time strictly hyperbolic equation with variable coe±cients in Cartesian product of the time interval and the spatial multidimensional torus. We establish the solvability of this problem in the Sobolev spaces scale for almost all (except for the set of a given small measure) vectors of coefficients in the nonlocal conditions. We prove the metric theorem of the lower estimation of small (nonlinear) denominators of the problem.