Neumann边值条件下的二维逆Sturm-Liouville问题

An Inverse Problem for Two Dimensional Vectorial Sturm-Liouville Equation Respect to Neumann Boundary Conditions

讨论二维的Sturm Liouville方程在Neumann边值条件下势函数的重构问题.设Q(x)是2×2的实对称+Q(x)的谱在不同条件下的性质,通矩阵值函数,利用紧算子的谱理论及留数知识得到了S L算子L=-d2dx2过这些性质的讨论得出:在一定的条件下可以唯一的确定势函数Q(x).

The reconstruction of a two dimensional vectorial Sturm-Liouville equation subject to Neumann boudary conditions is discussed.Let Q(x) be a 2×2 real symmetric matrix valued function.By inverstigating some properties of the spectra for two dimensional vectorial S-L operator -d^2dx^2+Q(x) related to different conditions,it proves that five spectra determine the potential function of the two dimensional vectorial S-L operator with the Neumann boundary condition uniquely.