二阶可积边值问题特征函数的渐近表示

Asymptotic representation of eigenfunctions for the second-order integrable boundary value problems

目的研究一类二阶可积边值问题特征函数的渐近估计式。方法借用打靶法思想,结合分析技巧。结果在势函数满足一定光滑性条件下得到了特征函数的高阶无穷小的渐近估计。结论特征函数及特征值的渐近估计式受到边界条件及势函数光滑性的影响。

Purposes—To study the asymptotic estimation formula of the eigenfunctions for the second-order integrable boundary value problems with integral condition.Methods—The shooting method and analytical technic are used for solving this problem.Result—Under the condition that the potential function satisfies certain smoothness is obtained the higher-order infinitesimal asymptotic estimation of the eigenfunction.Conclusion—The asymptotic estimations of eigenfunctions and eigenvalues are affected by boundary conditions and the smoothness of potential function.