论文标题
在Ambarzumyan型振动弦方程的逆问题上
On Ambarzumyan-type Inverse Problems of Vibrating String Equations
论文作者
论文摘要
我们考虑振动弦方程的反光谱理论。在这方面，陈述并证明了第一个特征值Ambarzumyan型唯一性定理，并受到分离的自我接触边界条件的约束。更确切地说，这表明边界参数域中有一条曲线，在其上不可能进行类似的类似物。确定了$ n $ th特征值的必要条件，该条件允许陈述定理。另外，检查了第一个特征值的几种特性。确定了下限和上限，并且在边界参数域中描述了区域，其中第一个特征值的符号保持不变。本文有助于频谱理论以及直接光谱理论。
We consider the inverse spectral theory of vibrating string equations. In this regard, first eigenvalue Ambarzumyan-type uniqueness theorems are stated and proved subject to separated, self-adjoint boundary conditions. More precisely, it is shown that there is a curve in the boundary parameters' domain on which no analog of it is possible. Necessary conditions of the $n$-th eigenvalue are identified, which allows to state the theorems. In addition, several properties of the first eigenvalue are examined. Lower and upper bounds are identified, and the areas are described in the boundary parameters' domain on which the sign of the first eigenvalue remains unchanged. This paper contributes to inverse spectral theory as well as to direct spectral theory.
