Multipoint Problem for a System of Hyperbolic Equations with Mixed Derivative

Abstract

We consider a multipoint problem with data lying on the characteristics of a system of hyperbolic equations of the second order with two independent variables. We introduce new unknown functions and reduce the problem to an equivalent problem formed by a family of multipoint problems for systems of ordinary differential equations and functional relations. We establish conditions for the existence of a unique solution in terms of the coefficients of multipoint problems.