标题： 第四阶微分算子类的Borg型定理 显示英文标题

标题： Borg-type theorem for a class of fourth-order differential operators

摘要： 在本文中，我们研究四阶微分方程$y^{(4)} - (p y')' + q y = \lambda y$的逆谱问题，其中实系数为$p$和$q$的$L^2(0,1)$。 我们证明，对于接近常数的系数，对应于狄利克雷和狄利克雷-诺伊曼边界条件的两个谱唯一确定$p$或$q$。 该结果将二阶情况的 Borg 定理扩展到了四阶情况。 显示英文摘要

摘要： In this paper, we study an inverse spectral problem for the fourth-order differential equation $y^{(4)} - (p y')' + q y = \lambda y$ with real-valued coefficients $p$ and $q$ of $L^2(0,1)$. We prove that, for near-constant coefficients, the two spectra corresponding to the Dirichlet and the Dirichlet-Neumann boundary conditions uniquely determine either $p$ or $q$. The result extends the Borg theorem of the second-order case to the fourth-order case.