On solutions of the Goursat problem for nonlinear hyperbolic differential equation in unbounded region

Abstract

We study the solvability of the Goursat problem for nonlinear hyperbolic partial differential equation in unbounded region. The method of the proof of the main result depends oil the construction of a special Banach space consisting of real functions being defined, continuous and tempered on a real half-axis and on applying the Schauder fixed point principle.