一类二阶微分方程的特征值估计及其反问题

Estimate of the Eigenvalue and Inverse Problem of a Class of Second-order Differential Equations

借助Rouché定理及渐近分析的方法,给出了边界条件含有特征参数的一类二阶微分方程的特征值渐近公式.运用特征值渐近公式给出了特征值反问题的一个惟一性结果及重构公式.

With the help of Rouché＇s theorem and the methods of asymptotic analysis,we give asymptotic formula of the eigenvalue of a class of second-order differential equations with eigenparameter contained in the bound ary conditions.A uniqueness result of inverse eigenvalue problem and reconstruc tions of h and k are presented.