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

作　　者：蔡日增[1] 吴建成[2] 

机构地区：[1]江南大学理学院,江苏无锡214064 [2]江苏工业学院信息科学系,江苏常州213016

出　　处：《江南大学学报（自然科学版）》2003年第4期423-426,共4页Joural of Jiangnan University (Natural Science Edition)　

摘　　要：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.

关 键 词：始值问题 重特征方程 离散现象 

分 类 号：O175.27[理学—数学]