中文摘要：

本文研究四阶边值问题的特征值对边界的依赖性问题,指出带有支撑边界条件的四阶边值问题的特征值连续且光滑地依赖于边界点,给出其第n个特征值关于一端点的一阶微分表达式,并证明当区间长度趋于零时,其所有的特征值会趋于无穷.

英文摘要：

In this paper we study the dependence of eigenvalues of fourth-order boundary value problems on the boundary. We show that the eigenvalues of fourth-order boundary value problems with supported ends depend not only continuously but smoothly on boundary points, and that the derivative of the nth eigenvalue as a function of an endpoint satisfies a first order differential equation. In addition, we prove that as the length of the interval shrinks to zero all higher eigenvalues march off to plus infinity.