关于某个四阶非对称微分方程边值问题的唯一性

On the Uniqueness of solution to Some Four-Order Nonsymmetric Differential Equation Boundary Problem

本文处理如下形式的四阶非对称微分方程边值问题的唯一性。 对于对称情形,传统的处理方法是利用Thichmarsh,E.C.的函数论方法与亏指标理论。而当方程为非对称时,上述方法会有些困难。但若通过构造某个特殊的与(?)λ有关的内积,并利用内插不等式及Opial不等式,则非对称情形能被容易地处理且得到许多唯一性的结果。

This paper deals with the uniqueness of- the solution to some four-order nonsymmetric differential equation boundary problem in the foliowingAccording to the classical technique for the symmetric differential operators, it can be tackled by using the E.C.Tichmarsh's functional method and the deficiency index theory.When the equation is nonsymmetric, it is somewhat difficult to use the above method. However, if some estimation techniques, especially interpolating inequality and Opial inequality, are used, and some special inner product connecting with Aλ is constructed, it can be solved with ease and a lot of results of uniqueness are obtained