A non-linear Goursat problem for a high order polyvibrating equation

Abstract

SynopsisThis paper proves the existence of a solution of a non-linear Goursat problem for a partial differential equation of order 2p (p ≧ 2) with the boundary conditions given on 2p curves emanating from a common point. The problem is reduced to a system of integro-differential-functional equations and then Schauder's fixed point theorem is applied.