振动弦方程的Ambarzumyan型反问题
On Ambarzumyan-type Inverse Problems of Vibrating String Equations
摘要：
我们考虑弦振动方程的逆谱理论。在这方面，第一特征值Ambarzumyan型唯一性定理的陈述和证明受到分离，自伴边界条件。更准确地说，它表明，有一个曲线在边界参数的域上，它是不可能的模拟。确定了$n$ -th特征值的必要条件，从而可以陈述定理。此外，第一特征值的几个性质进行了检查。确定了上、下界，并在第一特征值符号保持不变的边界参数域中描述了区域。本文有助于逆谱理论以及直接谱理论。
英文摘要：
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.
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