Abstract: This paper deals with the discrete phenomena in existence and uniqueness in the mixed problem with homogeneous boundary data in the equation the solution of the problem is not only unique but alsoexisting; if no uniqueness and existence can be found in the solution. In other words, only under some campatibility conditions and with some addi: tional data given to the double characteristic points (when x = 0) of the equation, can the solution of the problem be existing.