Abstract: This paper deals with the discrete phenomena in existence and uniqueness in the mixed problem with the second nonhomogeneous boundary condition in the equationuxx-x2utt+put=0. If p≠1, 5, 9, ……, the solution of the problem is not onlyunique but also existing. If p=1, 5, 9, ……, neither uniqueness nor existence canbe found in the solution. In other words, only under some compatible conditions and with some additional data given to the dual characteristic points (when x = 0) in the equation, can the solution of the problem be existing and unigue.