第4始值问题重特征方程存在性中的离散现象

On Discrete Phenomena in Existence of the Fourth Initial Value Problem

讨论了重特征方程Uxx-x2Utt+pUt=0的第4始值问题.证明了除去p的可数集S外问题的解不单是存在的,也是唯一的,对于p∈S,问题的唯一性被破坏了,存在性也不成立.或者更确切地说,在一定的相容条件下,并补充适当的数据,新的解才是存在唯一的.

The paper deals with discrete phenomena in existence and uniqueness of the fourth initial value problem for the following equations: U(xx)-x^2U(tt)+pUt=0, U(x,12βx^2)=0,β>1.It is proved that the problem has unique solution except for a countable set S of p and for p∈S. No uniqueness and existence can be found for the solution which cease to hold.In other words,the solution of the problem can only exist and be unique when some additional date are given and some compatibility conditions are satisfied.