On Uniqueness Questions for Hyperbolic Differential Equations

摘要

This note is concerned with questions of uniqueness, existence and convergence of successive approximations for a solution of an initial value problem, where zxy = f(x,y,z,z z ) and z(x,0), z(0,y) are assigned. There are obtained analogues of the Nagumo and Kamke criteria in the theory of ordinary differential equations. The method employed is related to the arguments used by Viswanatham to prove the convergence of successive approximations for ordinary differential equations under conditions similar to those in Kamke's general uniqueness theorem.