论文摘要
Dirac方程是指 B （dy/dx）+Q（x）y=λy,0<x<π,（0.1） 其中 p（x）,q（x）为[0,π]上的实值连续函数。加上边值条件 y1（0）sinα+y2（0）cosα=0,y1（π）sinβ+y2（π）cosβ=0 （0.2）构成Dirac方程的常型特征值问题,本文从（0.1）+（0.2）和（0.1）+（0.3）两个特征值问题出发,讨论特征值的反问题,（0.3）式如下所示: y1（0）sinγ+y2（0）cosγ=0,y1（π）sinβ+y2（π）cosβ=0 （0.3）这里α,β和γ是三个实数,α≠γ.首先获得了一族特征函数φn的规范系数αn与（0.1）+（0.2）的特征值λn和（0.1）+（0.3）的特征值μn的关系。并获得了规范系数αn的渐进估计。由规范系数αn与谱函数ρ（λ）之间的关系,将从双谱确定Dirac算子势函数的反问题转化为由谱函数确定Dirac算子势函数的反问题.最后证明双谱反问题的存在性及惟一性。
论文目录
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